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Complex topological features of reservoirs shape learning performances
in bio-inspired recurrent neural networks: Recurrent networks are a special class of artificial neural systems that use
their internal states to perform computing tasks for machine learning. One of
its state-of-the-art developments, i.e. reservoir computing (RC), uses the
internal structure -- usually a static network with random structure -- to map
an input signal into a nonlinear dynamical system defined in a higher
dimensional space. Reservoirs are characterized by nonlinear interactions among
their units and their ability to store information through recurrent loops,
allowing to train artificial systems to learn task-specific dynamics. However,
it is fundamentally unknown how the random topology of the reservoir affects
the learning performance. Here, we fill this gap by considering a battery of
synthetic networks -- characterized by different topological features -- and 45
empirical connectomes -- sampled from brain regions of organisms belonging to 8
different species -- to build the reservoir and testing the learning
performance against a prediction task with a variety of complex input signals.
We find nontrivial correlations between RC performances and both the number of
nodes and rank of the covariance matrix of activation states, with performance
depending on the nature -- stochastic or deterministic -- of input signals.
Remarkably, the modularity and the link density of the reservoir are found to
affect RC performances: these results cannot be predicted by models only
accounting for simple topological features of the reservoir. Overall, our
findings highlight that the complex topological features characterizing
biophysical computing systems such as connectomes can be used to design
efficient bio-inspired artificial neural networks. | cond-mat_dis-nn |
Universal Transport Dynamics of Complex Fluids: Thermal motion in complex fluids is a complicated stochastic process but
ubiquitously exhibits initial ballistic, intermediate sub-diffusive, and
long-time non-Gaussian diffusive motion, unless interrupted. Despite its
relevance to numerous dynamical processes of interest in modern science, a
unified, quantitative understanding of thermal motion in complex fluids remains
a long-standing problem. Here, we present a new transport equation and its
solutions, which yield a unified quantitative explanation of the mean square
displacement (MSD) and the non-Gaussian parameter (NGP) of various fluid
systems. We find the environment-coupled diffusion kernel and its time
correlation function are two essential quantities determining transport
dynamics of complex fluids. From our analysis, we construct a general, explicit
model of the complex fluid transport dynamics. This model quantitatively
explains not only the MSD and NGP, but also the time-dependent relaxation of
the displacement distribution for various systems. We introduce the concepts of
intrinsic disorder and extrinsic disorder that have distinct effects on
transport dynamics and different dependencies on temperature and density. This
work presents a new paradigm for quantitative understanding of transport and
transport-coupled processes in complex disordered media. | cond-mat_dis-nn |
Unlearning regularization for Boltzmann Machines: Boltzmann Machines (BMs) are graphical models with interconnected binary
units, employed for the unsupervised modeling of data distributions. When
trained on real data, BMs show the tendency to behave like critical systems,
displaying a high susceptibility of the model under a small rescaling of the
inferred parameters. This behaviour is not convenient for the purpose of
generating data, because it slows down the sampling process, and induces the
model to overfit the training-data. In this study, we introduce a
regularization method for BMs to improve the robustness of the model under
rescaling of the parameters. The new technique shares formal similarities with
the unlearning algorithm, an iterative procedure used to improve memory
associativity in Hopfield-like neural networks. We test our unlearning
regularization on synthetic data generated by two simple models, the
Curie-Weiss ferromagnetic model and the Sherrington-Kirkpatrick spin glass
model, and we show that it outperforms $L_p$-norm schemes. Finally, we discuss
the role of parameter initialization. | cond-mat_dis-nn |
Simplified dynamics for glass model: In spin glass models one can remove minimization of free energy by some order
parameter. One can consider hierarchy of order parameters. It is possible to
divide energy among these parts. We can consider relaxation process in glass
system phenomonologically, as exchange of energy between 2 parts. It is
possible to identify trap points in phase space. We suggest some
phenomonological approximation-truncated Langevine.
The mean field statics is used to introduce a phenomenologic dynamics as its
natural extension.
Purely kinetical phase transitions are investigated.. | cond-mat_dis-nn |
Anchored advected interfaces, Oslo model, and roughness at depinning: There is a plethora of 1-dimensional advected systems with an absorbing
boundary: the Toom model of anchored interfaces, the directed exclusion process
where in addition to diffusion particles and holes can jump over their right
neighbor, simple diffusion with advection, and Oslo sandpiles. All these models
share a roughness exponent of $\zeta=1/4$, while the dynamic exponent $z$
varies, depending on the observable. We show that for the first three models
$z=1$, $z=2$, and $z=1/2$ are realized, depending on the observable. The Oslo
model is apart with a conjectured dynamic exponent of $z=10/7$. Since the
height in the latter is the gradient of the position of a disordered elastic
string, this shows that $\zeta =5/4$ for a driven elastic string at depinning. | cond-mat_dis-nn |
Effect of Nuclear Quadrupole Interaction on the Relaxation in Amorphous
Solids: Recently it has been experimentally demonstrated that certain glasses display
an unexpected magnetic field dependence of the dielectric constant. In
particular, the echo technique experiments have shown that the echo amplitude
depends on the magnetic field. The analysis of these experiments results in the
conclusion that the effect seems to be related to the nuclear degrees of
freedom of tunneling systems. The interactions of a nuclear quadrupole
electrical moment with the crystal field and of a nuclear magnetic moment with
magnetic field transform the two-level tunneling systems inherent in amorphous
dielectrics into many-level tunneling systems. The fact that these features
show up at temperatures $T<100mK$, where the properties of amorphous materials
are governed by the long-range $R^{-3}$ interaction between tunneling systems,
suggests that this interaction is responsible for the magnetic field dependent
relaxation. We have developed a theory of many-body relaxation in an ensemble
of interacting many-level tunneling systems and show that the relaxation rate
is controlled by the magnetic field. The results obtained correlate with the
available experimental data. Our approach strongly supports the idea that the
nuclear quadrupole interaction is just the key for understanding the unusual
behavior of glasses in a magnetic field. | cond-mat_dis-nn |
Understanding spin glass transition as a dynamic phenomenon: Existing theories explain spin glass transition in terms of a phase
transition and order parameters, and assume the existence of a distinct spin
glass phase. In addition to problems related to clarifying the nature of this
phase, the common challenge is to explain profound dynamic effects. Here, we
propose that the main experimental results of spin glass transition can be
understood in an entirely dynamic picture, without a reference to a distinct
spin glass phase, phase transition and order parameters. In this theory, the
susceptibility cusp at the glass transition temperature is due to the dynamic
crossover between the high-temperature relaxational and low-temperature spin
wave, or elastic, regime. The crossover takes place when $t=\tau$, where $t$ is
observation time and $\tau$ is relaxation time. Time-dependent effects,
inconsistent with the phase transition approach, and the logarithmic increase
of $T_g$ with field frequency in particular, originate as the immediate
consequence of the proposed picture. We comment on the behavior of non-linear
susceptibility. In our discussion, we explore similarities between the spin and
structural glass transitions. | cond-mat_dis-nn |
Effective transport properties of conformal Voronoi-bounded columns via
recurrent boundary element expansions: Effective transport properties of heterogeneous structures are predicted by
geometric microstructural parameters, but these can be difficult to calculate.
Here, a boundary element code with a recurrent series method accurately and
efficiently determines the high order parameters of polygonal and conformal
prisms in regular two-dimensional lattices and Voronoi tessellations (VT). This
reveals that proximity to simpler estimates is associated with: centroidal VT
(cf random VT), compactness, and VT structures (cf similarly compact
semi-regular lattices). An error in previously reported values for triangular
lattices is noted. | cond-mat_dis-nn |
Electrodynamics of a Coulomb Glass in n-type Silicon: Optical measurements of the real and imaginary frequency dependent
conductivity of uncompensated n-type silicon are reported. The experiments are
done in the quantum limit, $ \hbar\omega > k_{B}T$, across a broad doping range
on the insulating side of the Metal-Insulator transition (MIT). The observed
low energy linear frequency dependence shows characteristics consistent with
theories of a Coulomb glass, but discrepancies exist in the relative magnitudes
of the real and imaginary components. At higher energies we observe a crossover
to a quadratic frequency dependence that is sharper than expected over the
entire dopant range. The concentration dependence gives evidence that the
Coulomb interaction energy is the relevant energy scale that determines this
crossover. | cond-mat_dis-nn |
Electromagnetic Waves Through Disordered Systems: Comparison Of
Intensity, Transmission And Conductance: We obtain the statistics of the intensity, transmission and conductance for
scalar electromagnetic waves propagating through a disordered collection of
scatterers. Our results show that the probability distribution for these
quantities, x, follow a universal form x^a Exp(-x^m) . This family of functions
includes the Rayleigh distribution (when a=0, m=1) and the Dirac delta function
(a -> Infinity), which are the expressions for intensity and transmission in
the diffusive regime neglecting correlations. Finally, we find simple
analytical expressions for the nth moment of the distributions and for to the
ratio of the moments of the intensity and transmission, which generalizes the
n! result valid in the above regime. | cond-mat_dis-nn |
Correlated Persistent Tunneling Currents in Glasses: Low temperature properties of glasses are derived within a generalized
tunneling model, considering the motion of charged particles on a closed path
in a double-well potential. The presence of a magnetic induction field B
violates the time reversal invariance due to the Aharonov-Bohm phase, and leads
to flux periodic energy levels. At low temperature, this effect is shown to be
strongly enhanced by dipole-dipole and elastic interactions between tunneling
systems and becomes measurable. Thus, the recently observed strong sensitivity
of the electric permittivity to weak magnetic fields can be explained. In
addition, superimposed oscillations as a function of the magnetic field are
predicted. | cond-mat_dis-nn |
Continuum Percolation on Disoriented Surfaces: the Problem of Permeable
Disks on a Klein Bottle: The percolation threshold and wrapping probability $R_{\infty}$ for the
two-dimensional problem of continuum percolation on the surface of a Klein
bottle have been calculated by the Monte Carlo method with the Newman--Ziff
algorithm for completely permeable disks. It has been shown that the
percolation threshold of disks on the Klein bottle coincides with the
percolation threshold of disks on the surface of a torus, indicating that this
threshold is topologically invariant. The scaling exponents determining
corrections to the wrapping probability and critical concentration owing to the
finite-size effects are also topologically invariant. At the same time, the
quantities $R_{\infty}$ are different for percolation on the torus and Klein
bottle and are apparently determined by the topology of the surface.
Furthermore, the difference between the $R_{\infty}$ values for the torus and
Klein bottle means that at least one of the percolation clusters is degenerate. | cond-mat_dis-nn |
Phase boundary near a magnetic percolation transition: Motivated by recent experimental observations [Phys. Rev. 96, 020407 (2017)]
on hexagonal ferrites, we revisit the phase diagrams of diluted magnets close
to the lattice percolation threshold. We perform large-scale Monte Carlo
simulations of XY and Heisenberg models on both simple cubic lattices and
lattices representing the crystal structure of the hexagonal ferrites. Close to
the percolation threshold $p_c$, we find that the magnetic ordering temperature
$T_c$ depends on the dilution $p$ via the power law $T_c \sim |p-p_c|^\phi$
with exponent $\phi=1.09$, in agreement with classical percolation theory.
However, this asymptotic critical region is very narrow, $|p-p_c| \lesssim
0.04$. Outside of it, the shape of the phase boundary is well described, over a
wide range of dilutions, by a nonuniversal power law with an exponent somewhat
below unity. Nonetheless, the percolation scenario does not reproduce the
experimentally observed relation $T_c \sim (x_c -x)^{2/3}$ in
PbFe$_{12-x}$Ga$_x$O$_{19}$. We discuss the generality of our findings as well
as implications for the physics of diluted hexagonal ferrites. | cond-mat_dis-nn |
Design of one-dimensional Lambertian diffusers of light: We describe a method for designing a one-dimensional random surface that acts
as a Lambertian diffuser. The method is tested by means of rigorous computer
simulations and is shown to yield the desired scattering pattern. | cond-mat_dis-nn |
Evidence for growth of collective excitations in glasses at low
temperatures: We present new data on the nonequilibrium acoustic response of glasses to an
applied dc electric field below 1K. When compared with the analogous dielectric
response of the same material, the acoustic data show, within experimental
precision, identical dependence on the perturbing field, but stronger
temperature dependence. These data are difficult to reconcile with simple
generalizations of the dipole gap model of two-level system (TLS) dielectric
response, unless we assume that as T is decreased, interaction-based TLS
collective effects increase. | cond-mat_dis-nn |
Quantum fluctuations in the transverse Ising spin glass model: A field
theory of random quantum spin systems: We develop a mean-field theory for random quantum spin systems using the spin
coherent state path integral representation. After the model is reduced to the
mean field one-body Hamiltonian, the integral is analyzed with the aid of
several methods such as the semiclassical method and the gauge transformation.
As an application we consider the Sherrington-Kirkpatrick model in a transverse
field. Using the Landau expansion and its improved versions, we give a detailed
analysis of the imaginary-time dependence of the order parameters. Integrating
out the quantum part of the order parameters, we obtain the effective
renormalized free energy written in terms of the classically defined order
parameters. Our method allows us to obtain the spin glass-paramagnetic phase
transition point $\Gamma/J\sim 1.62$ at T=0. | cond-mat_dis-nn |
On the origin of the $λ$-transition in liquid Sulphur: Developing a novel experimental technique, we applied photon correlation
spectroscopy using infrared radiation in liquid Sulphur around $T_\lambda$,
i.e. in the temperature range where an abrupt increase in viscosity by four
orders of magnitude is observed upon heating within few degrees. This allowed
us - overcoming photo-induced and absorption effects at visible wavelengths -
to reveal a chain relaxation process with characteristic time in the ms range.
These results do rehabilitate the validity of the Maxwell relation in Sulphur
from an apparent failure, allowing rationalizing the mechanical and
thermodynamic behavior of this system within a viscoelastic scenario. | cond-mat_dis-nn |
Magnetoresistance in semiconductor structures with hopping conductivity:
effects of random potential and generalization for the case of acceptor
states: We reconsider the theory of magnetoresistance in hopping semiconductors.
First, we have shown that the random potential of the background impurities
affects significantly preexponential factor of the tunneling amplitude which
becomes to be a short-range one in contrast to the long-range one for purely
Coulomb hopping centers. This factor to some extent suppresses the negative
interference magnetoresistance and can lead to its decrease with temperature
decrease which is in agreement with earlier experimental observations. We have
also extended the theoretical models of positive spin magnetoresistance, in
particular, related to a presence of doubly occupied states (corresponding to
the upper Hubbard band) to the case of acceptor states in 2D structures. We
have shown that this mechanism can dominate over classical wave-shrinkage
magnetoresistance at low temperatures. Our results are in semi-quantitative
agreement with experimental data. | cond-mat_dis-nn |
Quantitative field theory of the glass transition: We develop a full microscopic replica field theory of the dynamical
transition in glasses. By studying the soft modes that appear at the dynamical
temperature we obtain an effective theory for the critical fluctuations. This
analysis leads to several results: we give expressions for the mean field
critical exponents, and we study analytically the critical behavior of a set of
four-points correlation functions from which we can extract the dynamical
correlation length. Finally, we can obtain a Ginzburg criterion that states the
range of validity of our analysis. We compute all these quantities within the
Hypernetted Chain Approximation (HNC) for the Gibbs free energy and we find
results that are consistent with numerical simulations. | cond-mat_dis-nn |
A numerical study of the overlap probability distribution and its
sample-to-sample fluctuations in a mean-field model: In this paper we study the fluctuations of the probability distributions of
the overlap in mean field spin glasses in the presence of a magnetic field on
the De Almeida-Thouless line. We find that there is a large tail in the left
part of the distribution that is dominated by the contributions of rare
samples. Different techniques are used to examine the data and to stress on
different aspects of the contribution of rare samples. | cond-mat_dis-nn |
Spatial correlation functions and dynamical exponents in very large
samples of 4D spin glasses: The study of the low temperature phase of spin glass models by means of Monte
Carlo simulations is a challenging task, because of the very slow dynamics and
the severe finite size effects they show. By exploiting at the best the
capabilities of standard modern CPUs (especially the SSE instructions), we have
been able to simulate the four-dimensional (4D) Edwards-Anderson model with
Gaussian couplings up to sizes $L=70$ and for times long enough to accurately
measure the asymptotic behavior. By quenching systems of different sizes to the
the critical temperature and to temperatures in the whole low temperature
phase, we have been able to identify the regime where finite size effects are
negligible: $\xi(t) \lesssim L/7$. Our estimates for the dynamical exponent ($z
\simeq 1/T$) and for the replicon exponent ($\alpha \simeq 1.0$ and
$T$-independent), that controls the decay of the spatial correlation in the
zero-overlap sector, are consistent with the RSB theory, but the latter differs
from the theoretically conjectured value. | cond-mat_dis-nn |
Continuum Percolation on Disoriented Surfaces: the Problem of Permeable
Disks on a Klein Bottle: The percolation threshold and wrapping probability $R_{\infty}$ for the
two-dimensional problem of continuum percolation on the surface of a Klein
bottle have been calculated by the Monte Carlo method with the Newman--Ziff
algorithm for completely permeable disks. It has been shown that the
percolation threshold of disks on the Klein bottle coincides with the
percolation threshold of disks on the surface of a torus, indicating that this
threshold is topologically invariant. The scaling exponents determining
corrections to the wrapping probability and critical concentration owing to the
finite-size effects are also topologically invariant. At the same time, the
quantities $R_{\infty}$ are different for percolation on the torus and Klein
bottle and are apparently determined by the topology of the surface.
Furthermore, the difference between the $R_{\infty}$ values for the torus and
Klein bottle means that at least one of the percolation clusters is degenerate. | cond-mat_dis-nn |
Localization crossover and subdiffusive transport in a classical
facilitated network model of a disordered, interacting quantum spin chain: We consider the random-field Heisenberg model, a paradigmatic model for
many-body localization (MBL), and add a Markovian dephasing bath coupled to the
Anderson orbitals of the model's non-interacting limit. We map this system to a
classical facilitated hopping model that is computationally tractable for large
system sizes, and investigate its dynamics. The classical model exhibits a
robust crossover between an ergodic (thermal) phase and a frozen (localized)
phase. The frozen phase is destabilized by thermal subregions (bubbles), which
thermalize surrounding sites by providing a fluctuating interaction energy and
so enable off-resonance particle transport. Investigating steady state
transport, we observe that the interplay between thermal and frozen bubbles
leads to a clear transition between diffusive and subdiffusive regimes. This
phenomenology both describes the MBL system coupled to a bath, and provides a
classical analogue for the many-body localization transition in the
corresponding quantum model, in that the classical model displays long local
memory times. It also highlights the importance of the details of the bath
coupling in studies of MBL systems coupled to thermal environments. | cond-mat_dis-nn |
Annealed inhomogeneities in random ferromagnets: We consider spin models on complex networks frequently used to model social
and technological systems. We study the annealed ferromagnetic Ising model for
random networks with either independent edges (Erd\H{o}s-R\'enyi), or with
prescribed degree distributions (configuration model). Contrary to many
physical models, the annealed setting is poorly understood and behaves quite
differently than the quenched system. In annealed networks with a fluctuating
number of edges, the Ising model changes the degree distribution, an aspect
previously ignored. For random networks with Poissonian degrees, this gives
rise to three distinct annealed critical temperatures depending on the precise
model choice, only one of which reproduces the quenched one. In particular, two
of these annealed critical temperatures are finite even when the quenched one
is infinite, since then the annealed graph creates a giant component for all
sufficiently small temperatures. We see that the critical exponents in the
configuration model with deterministic degrees are the same as the quenched
ones, which are the mean-field exponents if the degree distribution has finite
fourth moment, and power-law-dependent critical exponents otherwise.
Remarkably, the annealing for the configuration model with random i.i.d.
degrees washes away the universality class with power-law critical exponents. | cond-mat_dis-nn |
Metal-Insulator-Transition in a Weakly interacting Disordered Electron
System: The interplay of interactions and disorder is studied using the
Anderson-Hubbard model within the typical medium dynamical cluster
approximation. Treating the interacting, non-local cluster self-energy
($\Sigma_c[{\cal \tilde{G}}](i,j\neq i)$) up to second order in the
perturbation expansion of interactions, $U^2$, with a systematic incorporation
of non-local spatial correlations and diagonal disorder, we explore the initial
effects of electron interactions ($U$) in three dimensions. We find that the
critical disorder strength ($W_c^U$), required to localize all states,
increases with increasing $U$; implying that the metallic phase is stabilized
by interactions. Using our results, we predict a soft pseudogap at the
intermediate $W$ close to $W_c^U$ and demonstrate that the mobility edge
($\omega_\epsilon$) is preserved as long as the chemical potential, $\mu$, is
at or beyond the mobility edge energy. | cond-mat_dis-nn |
Enhancement of the Magnetocaloric Effect in Geometrically Frustrated
Cluster Spin Glass Systems: In this work, we theoretically demonstrate that a strong enhancement of the
Magnetocaloric Effect is achieved in geometrically frustrated cluster
spin-glass systems just above the freezing temperature. We consider a network
of clusters interacting randomly which have triangular structure composed of
Ising spins interacting antiferromagnetically. The intercluster disorder
problem is treated using a cluster spin glass mean-field theory, which allows
exact solution of the disordered problem. The intracluster part can be solved
using exact enumeration. The coupling between the inter and intracluster
problem incorporates the interplay between effects coming from geometric
frustration and disorder. As a result, it is shown that there is the onset of
cluster spin glass phase even with very weak disorder. Remarkably, it is
exactly within a range of very weak disorder and small magnetic field that is
observed the strongest isothermal release of entropy. | cond-mat_dis-nn |
Calculation of ground states of four-dimensional +or- J Ising spin
glasses: Ground states of four-dimensional (d=4) EA Ising spin glasses are calculated
for sizes up to 7x7x7x7 using a combination of a genetic algorithm and
cluster-exact approximation. The ground-state energy of the infinite system is
extrapolated as e_0=-2.095(1). The ground-state stiffness (or domain wall)
energy D is calculated. A D~L^{\Theta} behavior with \Theta=0.65(4) is found
which confirms that the d=4 model has an equilibrium spin-glass-paramagnet
transition for non-zero T_c. | cond-mat_dis-nn |
Adaptive Density-Matrix Renormalization-Group study of the disordered
antiferromagnetic spin-1/2 Heisenberg chain: Using the recently introduced adaptive density-matrix renormalization-group
method, we study the many spin-spin correlations of the spin-$1/2$
antiferromagnetic Heisenberg chain with random coupling constants, namely, the
mean value of the bulk and of the end-to-end correlations, the typical value of
the bulk correlations, and the distribution of the bulk correlations. Our
results are in striking agreement with the predictions of the strong-disorder
renormalization group method. We do not find any hint of logarithmic
corrections neither in the bulk average correlations, which were recently
reported by Shu et al. [Phys. Rev. B 94,174442 (2016)], nor in the end-to-end
average correlations. We report computed the existence of logarithmic
correction on the end-to-end correlations of the clean chain. Finally, we have
determined that the distribution of the bulk correlations, when properly
rescaled by an associated Lyapunov exponent, is a narrow and universal
(disorder-independent) probability function. | cond-mat_dis-nn |
Effect of selection on ancestry: an exactly soluble case and its
phenomenological generalization: We consider a family of models describing the evolution under selection of a
population whose dynamics can be related to the propagation of noisy traveling
waves. For one particular model, that we shall call the exponential model, the
properties of the traveling wave front can be calculated exactly, as well as
the statistics of the genealogy of the population. One striking result is that,
for this particular model, the genealogical trees have the same statistics as
the trees of replicas in the Parisi mean-field theory of spin glasses. We also
find that in the exponential model, the coalescence times along these trees
grow like the logarithm of the population size. A phenomenological picture of
the propagation of wave fronts that we introduced in a previous work, as well
as our numerical data, suggest that these statistics remain valid for a larger
class of models, while the coalescence times grow like the cube of the
logarithm of the population size. | cond-mat_dis-nn |
Efficient Representation of Quantum Many-body States with Deep Neural
Networks: The challenge of quantum many-body problems comes from the difficulty to
represent large-scale quantum states, which in general requires an
exponentially large number of parameters. Recently, a connection has been made
between quantum many-body states and the neural network representation
(\textit{arXiv:1606.02318}). An important open question is what characterizes
the representational power of deep and shallow neural networks, which is of
fundamental interest due to popularity of the deep learning methods. Here, we
give a rigorous proof that a deep neural network can efficiently represent most
physical states, including those generated by any polynomial size quantum
circuits or ground states of many body Hamiltonians with polynomial-size gaps,
while a shallow network through a restricted Boltzmann machine cannot
efficiently represent those states unless the polynomial hierarchy in
computational complexity theory collapses. | cond-mat_dis-nn |
Topological phases and Anderson localization in off-diagonal mosaic
lattices: We introduce a one-dimensional lattice model whose hopping amplitudes are
modulated for equally spaced sites. Such mosaic lattice exhibits many
interesting topological and localization phenomena that do not exist in the
regular off-diagonal lattices. When the mosaic modulation is commensurate with
the underlying lattice, topologically nontrivial phases with zero- and
nonzero-energy edge modes are observed as we tune the modulation, where the
nontrivial regimes are characterized by quantized Berry phases. If the mosaic
lattice becomes incommensurate, Anderson localization will be induced purely by
the quasiperiodic off-diagonal modulations. The localized eigenstate is found
to be centered on two neighboring sites connected by the quasiperiodic hopping
terms. Furthermore, both the commensurate and incommensurate off-diagonal
mosaic lattices can host Chern insulators in their two-dimensional
generalizations. Our work provides a platform for exploring topological phases
and Anderson localization in low-dimensional systems. | cond-mat_dis-nn |
Enhancement of chaotic subdiffusion in disordered ladders with synthetic
gauge fields: We study spreading wave packets in a disordered nonlinear ladder with broken
time-reversal symmetry induced by synthetic gauge fields. The model describes
the dynamics of interacting bosons in a disordered and driven optical ladder
within a mean-field approximation. The second moment of the wave packet $m_{2}
= g t^{\alpha}$ grows subdiffusively with the universal exponent $\alpha \simeq
1/3$ similar to the time-reversal case. However the prefactor $g$ is strongly
modified by the field strength and shows a non-monotonic dependence. For a weak
field, the prefactor increases since time-reversal enhanced backscattering is
suppressed. For strong fields the spectrum of the linear wave equation reduces
the localization length through the formation of gaps and narrow bands.
Consequently the prefactor for the subdiffusive spreading law is suppressed. | cond-mat_dis-nn |
Avalanches and many-body resonances in many-body localized systems: We numerically study both the avalanche instability and many-body resonances
in strongly-disordered spin chains exhibiting many-body localization (MBL). We
distinguish between a finite-size/time MBL regime, and the asymptotic MBL
phase, and identify some "landmarks" within the MBL regime. Our first landmark
is an estimate of where the MBL phase becomes unstable to avalanches, obtained
by measuring the slowest relaxation rate of a finite chain coupled to an
infinite bath at one end. Our estimates indicate that the actual MBL-to-thermal
phase transition, in infinite-length systems, occurs much deeper in the MBL
regime than has been suggested by most previous studies. Our other landmarks
involve system-wide resonances. We find that the effective matrix elements
producing eigenstates with system-wide resonances are enormously broadly
distributed. This means that the onset of such resonances in typical samples
occurs quite deep in the MBL regime, and the first such resonances typically
involve rare pairs of eigenstates that are farther apart in energy than the
minimum gap. Thus we find that the resonance properties define two landmarks
that divide the MBL regime in to three subregimes: (i) at strongest disorder,
typical samples do not have any eigenstates that are involved in system-wide
many-body resonances; (ii) there is a substantial intermediate regime where
typical samples do have such resonances, but the pair of eigenstates with the
minimum spectral gap does not; and (iii) in the weaker randomness regime, the
minimum gap is involved in a many-body resonance and thus subject to level
repulsion. Nevertheless, even in this third subregime, all but a vanishing
fraction of eigenstates remain non-resonant and the system thus still appears
MBL in many respects. Based on our estimates of the location of the avalanche
instability, it might be that the MBL phase is only part of subregime (i). | cond-mat_dis-nn |
A pragmatical access to the viscous flow: The paper derives a relation for the viscosity of undercooled liquids on the
basis of the pragmatical model concept of Eshelby relaxations with a finite
lifetime. From accurate shear relaxation data in the literature, one finds that
slightly less than half of the internal stresses relax directly via single
Eshelby relaxations; the larger part dissolves at the terminal lifetime, which
is a combined effect of many Eshelby relaxations. | cond-mat_dis-nn |
Monte Carlo studies of the one-dimensional Ising spin glass with
power-law interactions: We present results from Monte Carlo simulations of the one-dimensional Ising
spin glass with power-law interactions at low temperature, using the parallel
tempering Monte Carlo method. For a set of parameters where the long-range part
of the interaction is relevant, we find evidence for large-scale droplet-like
excitations with an energy that is independent of system size, consistent with
replica symmetry breaking. We also perform zero-temperature defect energy
calculations for a range of parameters and find a stiffness exponent for domain
walls in reasonable, but by no means perfect agreement with analytic
predictions. | cond-mat_dis-nn |
Fixed points and their stability in the functional renormalization group
of random field models: We consider the zero-temperature fixed points controlling the critical
behavior of the $d$-dimensional random-field Ising, and more generally $O(N)$,
models. We clarify the nature of these fixed points and their stability in the
region of the $(N,d)$ plane where one passes from a critical behavior
satisfying the $d\rightarrow d-2$ dimensional reduction to one where it breaks
down due to the appearance of strong enough nonanalyticities in the functional
dependence of the cumulants of the renormalized disorder. We unveil an
intricate and unusual behavior. | cond-mat_dis-nn |
Equilibrium valleys in spin glasses at low temperature: We investigate the 3-dimensional Edwards-Anderson spin glass model at low
temperature on simple cubic lattices of sizes up to L=12. Our findings show a
strong continuity among T>0 physical features and those found previously at
T=0, leading to a scenario with emerging mean field like characteristics that
are enhanced in the large volume limit. For instance, the picture of space
filling sponges seems to survive in the large volume limit at T>0, while
entropic effects play a crucial role in determining the free-energy degeneracy
of our finite volume states. All of our analysis is applied to equilibrium
configurations obtained by a parallel tempering on 512 different disorder
realizations. First, we consider the spatial properties of the sites where
pairs of independent spin configurations differ and we introduce a modified
spin overlap distribution which exhibits a non-trivial limit for large L.
Second, after removing the Z_2 (+-1) symmetry, we cluster spin configurations
into valleys. On average these valleys have free-energy differences of O(1),
but a difference in the (extensive) internal energy that grows significantly
with L; there is thus a large interplay between energy and entropy
fluctuations. We also find that valleys typically differ by sponge-like space
filling clusters, just as found previously for low-energy system-size
excitations above the ground state. | cond-mat_dis-nn |
Density of States near the Anderson Transition in a Four-dimensional
Space. Renormalizable Models: Asymptotically exact results are obtained for the average Green function and
density of states of a disordered system for a renormalizable class of models
(as opposed to the lattice models examined previously [Zh. Eksp. Teor. Fiz. 106
(1994) 560-584]). For N\sim 1 (where N is an order of the perturbation theory),
only the parquet terms corresponding to the highest powers of large logarithms
are retained. For large N, this approximation is inadequate because of the fast
growth with N of the coefficients for the lower powers of the logarithms. The
latter coefficients are calculated in the leading order in N from the
Callan-Symanzik equation with results of the Lipatov method using as boundary
conditions. For calculating the self-energy at finite momentum, a modification
of the parquet approximation is used, that allows the calculations to be done
in an arbitrary finite logarithmic approximation but in the leading order in N.
It is shown that the phase transition point shifts in the complex plane,
thereby insuring regularity of the density of states for all energies. The
"spurious" pole is avoided in such a way that effective interaction remains
logarithmically weak. | cond-mat_dis-nn |
Zero-Temperature Critical Phenomena in Two-Dimensional Spin Glasses: Recent developments in study of two-dimensional spin glass models are
reviewed in light of fractal nature of droplets at zero-temperature. Also
presented are some new results including a new estimate of the stiffness
exponent using a boundary condition different from conventional ones. | cond-mat_dis-nn |
Quasi-long range order in the random anisotropy Heisenberg model: The large distance behaviors of the random field and random anisotropy
Heisenberg models are studied with the functional renormalization group in
$4-\epsilon$ dimensions. The random anisotropy model is found to have a phase
with the infinite correlation radius at low temperatures and weak disorder. The
correlation function of the magnetization obeys a power law $<{\bf m}({\bf
r}_1) {\bf m}({\bf r}_2)>\sim| {\bf r}_1-{\bf r}_2|^{-0.62\epsilon}$. The
magnetic susceptibility diverges at low fields as $\chi\sim
H^{-1+0.15\epsilon}$. In the random field model the correlation radius is found
to be finite at the arbitrarily weak disorder. | cond-mat_dis-nn |
Comment on "Evidence of Non-Mean-Field-Like Low-Temperature Behavior in
the Edwards-Anderson Spin-Glass Model": A recent interesting paper [Yucesoy et al. Phys. Rev. Lett. 109, 177204
(2012), arXiv:1206:0783] compares the low-temperature phase of the 3D
Edwards-Anderson (EA) model to its mean-field counterpart, the
Sherrington-Kirkpatrick (SK) model. The authors study the overlap distributions
P_J(q) and conclude that the two models behave differently. Here we notice that
a similar analysis using state-of-the-art, larger data sets for the EA model
(generated with the Janus computer) leads to a very clear interpretation of the
results of Yucesoy et al., showing that the EA model behaves as predicted by
the replica symmetry breaking (RSB) theory. | cond-mat_dis-nn |
Solvable model of a polymer in random media with long ranged disorder
correlations: We present an exactly solvable model of a Gaussian (flexible) polymer chain
in a quenched random medium. This is the case when the random medium obeys very
long range quadratic correlations. The model is solved in $d$ spatial
dimensions using the replica method, and practically all the physical
properties of the chain can be found. In particular the difference between the
behavior of a chain that is free to move and a chain with one end fixed is
elucidated. The interesting finding is that a chain that is free to move in a
quadratically correlated random potential behaves like a free chain with $R^2
\sim L$, where $R$ is the end to end distance and $L$ is the length of the
chain, whereas for a chain anchored at one end $R^2 \sim L^4$. The exact
results are found to agree with an alternative numerical solution in $d=1$
dimensions. The crossover from long ranged to short ranged correlations of the
disorder is also explored. | cond-mat_dis-nn |
Metal-insulator transition in hydrogenated graphene as manifestation of
quasiparticle spectrum rearrangement of anomalous type: We demonstrate that the spectrum rearrangement can be considered as a
precursor of the metal-insulator transition observed in graphene dosed with
hydrogen atoms. The Anderson-type transition is attributed to the coincidence
between the Fermi level and the mobility edge, which appearance is induced by
the spectrum rearrangement. Available experimental data are thoroughly compared
to the theoretical results for the Lifshitz impurity model. | cond-mat_dis-nn |
Virtual Node Graph Neural Network for Full Phonon Prediction: The structure-property relationship plays a central role in materials
science. Understanding the structure-property relationship in solid-state
materials is crucial for structure design with optimized properties. The past
few years witnessed remarkable progress in correlating structures with
properties in crystalline materials, such as machine learning methods and
particularly graph neural networks as a natural representation of crystal
structures. However, significant challenges remain, including predicting
properties with complex unit cells input and material-dependent,
variable-length output. Here we present the virtual node graph neural network
to address the challenges. By developing three types of virtual node approaches
- the vector, matrix, and momentum-dependent matrix virtual nodes, we achieve
direct prediction of $\Gamma$-phonon spectra and full dispersion only using
atomic coordinates as input. We validate the phonon bandstructures on various
alloy systems, and further build a $\Gamma$-phonon database containing over
146,000 materials in the Materials Project. Our work provides an avenue for
rapid and high-quality prediction of phonon spectra and bandstructures in
complex materials, and enables materials design with superior phonon properties
for energy applications. The virtual node augmentation of graph neural networks
also sheds light on designing other functional properties with a new level of
flexibility. | cond-mat_dis-nn |
On the Dynamics of Glassy Systems: Glassy systems are disordered systems characterized by extremely slow
dynamics. Examples are supercooled liquids, whose dynamics slow down under
cooling. The specific pattern of slowing-down depends on the material
considered. This dependence is poorly understood, in particular, it remains
generally unclear which aspects of the microscopic structures control the
dynamics and other macroscopic properties. Attacking this question is one of
the two main aspects of this dissertation. We have introduced a new class of
models of supercooled liquids, which captures the central aspects of the
correspondence between structure and elasticity on the one hand, the
correlation of structure and thermodynamic and dynamic properties on the other.
Our results shed new light on the temperature-dependence of the topology of
covalent networks, in particular, on the rigidity transition that occurs when
the valence is increased.
Other questions appear in glassy systems at zero temperature. In that
situation, a glassy system can flow if an external driving force is imposed
above some threshold. The first example we will consider is the erosion of a
riverbed. Experiments support the existence of a threshold forcing, below which
no erosion flux is observed. In this dissertation, we present a novel
microscopic model to describe the erosion near threshold. This model makes new
quantitative predictions for the spatial reparation of the flux. To study
further the self-organization of driven glassy systems, we investigate the
athermal dynamics of mean-field spin glasses. The spin glass self-organizes
into the configurations that are stable, but barely so. Such marginal stability
appears with the presence of a pseudogap in soft excitations. We show that the
emergence of a pseudogap is deeply related to very strong anti-correlations
emerging among soft excitations. | cond-mat_dis-nn |
Critical properties of the Anderson localization transition and the high
dimensional limit: In this paper we present a thorough study of transport, spectral and
wave-function properties at the Anderson localization critical point in spatial
dimensions $d = 3$, $4$, $5$, $6$. Our aim is to analyze the dimensional
dependence and to asses the role of the $d\rightarrow \infty$ limit provided by
Bethe lattices and tree-like structures. Our results strongly suggest that the
upper critical dimension of Anderson localization is infinite. Furthermore, we
find that the $d_U=\infty$ is a much better starting point compared to $d_L=2$
to describe even three dimensional systems. We find that critical properties
and finite size scaling behavior approach by increasing $d$ the ones found for
Bethe lattices: the critical state becomes an insulator characterized by
Poisson statistics and corrections to the thermodynamics limit become
logarithmic in $N$. In the conclusion, we present physical consequences of our
results, propose connections with the non-ergodic delocalised phase suggested
for the Anderson model on infinite dimensional lattices and discuss
perspectives for future research studies. | cond-mat_dis-nn |
Linear theory of random textures of 3He-A in aerogel: Spacial variation of the orbital part of the order parameter of $^3$He-A in
aerogel is represented as a random walk of the unit vector $\mathbf{l}$ in a
field of random anisotropy produced by the strands of aerogel. For a range of
distances, where variation of $\mathbf{l}$ is small in comparison with its
absolute value correlation function of directions of $\mathbf{l}(\mathbf{r})$
is expressed in terms of the correlation function of the random anisotropy
field. With simplifying assumptions about this correlation function a spatial
dependence of the average variation $\langle\delta\mathbf{l}^2\rangle$ is found
analytically for isotropic and axially anisotropic aerogels. Average
projections of $\mathbf{l}$ on the axes of anisotropy are expressed in terms of
characteristic parameters of the problem. Within the "model of random
cylinders" numerical estimations of characteristic length for disruption of the
long-range order and of the critical anisotropy for restoration of this order
are made and compared with other estimations . | cond-mat_dis-nn |
KPZ equation in one dimension and line ensembles: For suitably discretized versions of the Kardar-Parisi-Zhang equation in one
space dimension exact scaling functions are available, amongst them the
stationary two-point function. We explain one central piece from the technology
through which such results are obtained, namely the method of line ensembles
with purely entropic repulsion. | cond-mat_dis-nn |
Structure and Time-Evolution of an Internet Dating Community: We present statistics for the structure and time-evolution of a network
constructed from user activity in an Internet community. The vastness and
precise time resolution of an Internet community offers unique possibilities to
monitor social network formation and dynamics. Time evolution of well-known
quantities, such as clustering, mixing (degree-degree correlations), average
geodesic length, degree, and reciprocity is studied. In contrast to earlier
analyses of scientific collaboration networks, mixing by degree between
vertices is found to be disassortative. Furthermore, both the evolutionary
trajectories of the average geodesic length and of the clustering coefficients
are found to have minima. | cond-mat_dis-nn |
Epidemic spread in weighted networks: We study the detailed epidemic spreading process in scale-free networks with
weight that denote familiarity between two people or computers. The result
shows that spreading velocity reaches a peak quickly then decays representing
power-law time behavior, and comparing to non-weighted networks, precise
hierarchical dynamics is not found although the nodes with larger strength is
preferential to be infected. | cond-mat_dis-nn |
Structural Probe of a Glass Forming Liquid: Generalized Compressibility: We introduce a new quantity to probe the glass transition. This quantity is a
linear generalized compressibility which depends solely on the positions of the
particles. We have performed a molecular dynamics simulation on a glass forming
liquid consisting of a two component mixture of soft spheres in three
dimensions. As the temperature is lowered (or as the density is increased), the
generalized compressibility drops sharply at the glass transition, with the
drop becoming more and more abrupt as the measurement time increases. At our
longest measurement times, the drop occurs approximately at the mode coupling
temperature $T_C$. The drop in the linear generalized compressibility occurs at
the same temperature as the peak in the specific heat. By examining the
inherent structure energy as a function of temperature, we find that our
results are consistent with the kinetic view of the glass transition in which
the system falls out of equilibrium. We find no size dependence and no evidence
for a second order phase transition though this does not exclude the
possibility of a phase transition below the observed glass transition
temperature. We discuss the relation between the linear generalized
compressibility and the ordinary isothermal compressibility as well as the
static structure factor. | cond-mat_dis-nn |
Validity of the zero-thermodynamic law in off-equilibrium coupled
harmonic oscillators: In order to describe the thermodynamics of the glassy systems it has been
recently introduced an extra parameter also called effective temperature which
generalizes the fluctuation-dissipation theorem (FDT) to systems
off-equilibrium and supposedly describes thermal fluctuations around the aging
state. Here we investigate the applicability of a zero-th law for
non-equilibrium glassy systems based on these effective temperatures by
studying two coupled subsystems of harmonic oscillators with Monte Carlo
dynamics. We analyze in detail two types of dynamics: 1) sequential dynamics
where the coupling between the subsystems comes only from the Hamiltonian and
2) parallel dynamics where there is a further coupling between the subsystems
arising from the dynamics. We show that the coupling described in the first
case is not enough to make asymptotically the effective temperatures of two
interacting subsystems coincide, the reason being the too small thermal
conductivity between them in the aging state. This explains why different
interacting degrees of freedom in structural glasses may stay at different
effective temperatures without never mutually thermalizing. | cond-mat_dis-nn |
Crystal-like Order Stabilizing Glasses: Structural Origin of
Ultra-stable Metallic Glasses: Glasses are featured with a disordered amorphous structure, being opposite to
crystals that are constituted by periodic lattices. In this study we report
that the exceptional thermodynamic and kinetic stability of an ultra-stable
binary ZrCu metallic glass, fabricated by high-temperature physical vapor
deposition, originates from ubiquitous crystal-like medium range order (MRO)
constituted by Voronoi polyhedron ordering with well-defined local
translational symmetry beyond nearest atomic neighbors. The crystal-like MRO
significantly improves the thermodynamic and kinetic stability of the glass,
which is in opposition to the conventional wisdom that crystal-like order
deteriorates the stability and forming ability of metallic glasses. This study
unveils the structural origin of ultra-stable metallic glasses and shines a
light on the intrinsic correlation of local atomic structure ordering with
glass transition of metallic glasses. | cond-mat_dis-nn |
Origin of the Growing Length Scale in M-p-Spin Glass Models: Two versions of the M-p-spin glass model have been studied with the
Migdal-Kadanoff renormalization group approximation. The model with p=3 and M=3
has at mean-field level the ideal glass transition at the Kauzmann temperature
and at lower temperatures still the Gardner transition to a state like that of
an Ising spin glass in a field. The model with p=3 and M=2 has only the Gardner
transition. In the dimensions studied, d=2,3 and 4, both models behave almost
identically, indicating that the growing correlation length as the temperature
is reduced in these models -- the analogue of the point-to-set length scale --
is not due to the mechanism postulated in the random first order transition
theory of glasses, but is more like that expected on the analogy of glasses to
the Ising spin glass in a field. | cond-mat_dis-nn |
Universality and Deviations in Disordered Systems: We compute the probability of positive large deviations of the free energy
per spin in mean-field Spin-Glass models. The probability vanishes in the
thermodynamic limit as $P(\Delta f) \propto \exp[-N^2 L_2(\Delta f)]$. For the
Sherrington-Kirkpatrick model we find $L_2(\Delta f)=O(\Delta f)^{12/5}$ in
good agreement with numerical data and with the assumption that typical small
deviations of the free energy scale as $N^{1/6}$. For the spherical model we
find $L_2(\Delta f)=O(\Delta f)^{3}$ in agreement with recent findings on the
fluctuations of the largest eigenvalue of random Gaussian matrices. The
computation is based on a loop expansion in replica space and the non-gaussian
behaviour follows in both cases from the fact that the expansion is divergent
at all orders. The factors of the leading order terms are obtained resumming
appropriately the loop expansion and display universality, pointing to the
existence of a single universal distribution describing the small deviations of
any model in the full-Replica-Symmetry-Breaking class. | cond-mat_dis-nn |
On the Paramagnetic Impurity Concentration of Silicate Glasses from
Low-Temperature Physics: The concentration of paramagnetic trace impurities in glasses can be
determined via precise SQUID measurements of the sample's magnetization in a
magnetic field. However the existence of quasi-ordered structural
inhomogeneities in the disordered solid causes correlated tunneling currents
that can contribute to the magnetization, surprisingly, also at the higher
temperatures. We show that taking into account such tunneling systems gives
rise to a good agreement between the concentrations extracted from SQUID
magnetization and those extracted from low-temperature heat capacity
measurements. Without suitable inclusion of such magnetization contribution
from the tunneling currents we find that the concentration of paramagnetic
impurities gets considerably over-estimated. This analysis represents a further
positive test for the structural inhomogeneity theory of the magnetic effects
in the cold glasses. | cond-mat_dis-nn |
Large-scale dynamical simulations of the three-dimensional XY spin glass: Large-scale simulations have been performed in the current-driven
three-dimensional XY spin glass with resistively-shunted junction dynamics for
sample sizes up to $64^3$. It is observed that the linear resistivity at low
temperatures tends to zero, providing a strong evidence of a finite temperature
phase-coherence (i.e. spin-glass) transition. Dynamical scaling analysis
demonstrates that a perfect collapse of current-voltage data can be achieved.
The obtained critical exponents agree with those in equilibrium Monte Carlo
simulations, and are compatible with those observed in various experiments on
high-T$_c$ cuprate superconductors. It is suggested that the spin and the
chirality order simultaneously. A genuine continuous depinning transition is
found at zero temperature. For low temperature creep motion, critical exponents
are evaluated, and a non-Arrhenius creep motion is observed in the low
temperature ordered phase. It is proposed that the XY spin glass gives an
effective description of the transport properties in high-T$_c$ superconductors
with d-wave symmetry. | cond-mat_dis-nn |
$1/f^α$ noise and generalized diffusion in random Heisenberg spin
systems: We study the `flux noise' spectrum of random-bond quantum Heisenberg spin
systems using a real-space renormalization group (RSRG) procedure that accounts
for both the renormalization of the system Hamiltonian and of a generic probe
that measures the noise. For spin chains, we find that the dynamical structure
factor $S_q(f)$, at finite wave-vector $q$, exhibits a power-law behavior both
at high and low frequencies $f$, with exponents that are connected to one
another and to an anomalous dynamical exponent through relations that differ at
$T = 0$ and $T = \infty$. The low-frequency power-law behavior of the structure
factor is inherited by any generic probe with a finite band-width and is of the
form $1/f^\alpha$ with $0.5 < \alpha < 1$. An analytical calculation of the
structure factor, assuming a limiting distribution of the RG flow parameters
(spin size, length, bond strength) confirms numerical findings. More generally,
we demonstrate that this form of the structure factor, at high temperatures, is
a manifestation of anomalous diffusion which directly follows from a
generalized spin-diffusion propagator. We also argue that $1/f$-noise is
intimately connected to many-body-localization at finite temperatures. In two
dimensions, the RG procedure is less reliable; however, it becomes convergent
for quasi-one-dimensional geometries where we find that one-dimensional
$1/f^\alpha$ behavior is recovered at low frequencies; the latter
configurations are likely representative of paramagnetic spin networks that
produce $1/f^\alpha$ noise in SQUIDs. | cond-mat_dis-nn |
Percolation of optical excitation mediated by near-field interactions: Optical excitation transfer in nanostructured matter has been intensively
studied in various material systems for versatile applications. Herein, we
discuss the percolation of optical excitations in randomly organized
nanostructures caused by optical near-field interactions governed by Yukawa
potential in a two-dimensional stochastic model. The model results demonstrate
the appearance of two phases of percolation of optical excitation as a function
of the localization degree of near-field interaction. Moreover, it indicates
sublinear scaling with percolation distance when the light localization is
strong. The results provide fundamental insights into optical excitation
transfer and will facilitate the design and analysis of nanoscale
signal-transfer characteristics. | cond-mat_dis-nn |
From particles to spins: Eulerian formulation of supercooled liquids and
glasses: The dynamics of supercooled liquid and glassy systems are usually studied
within the Lagrangian representation, in which the positions and velocities of
distinguishable interacting particles are followed. Within this representation,
however, it is difficult to define measures of spatial heterogeneities in the
dynamics, as particles move in and out of any one given region within long
enough times. It is also non-transparent how to make connections between the
structural glass and the spin glass problems within the Lagrangian formulation.
We propose an Eulerian formulation of supercooled liquids and glasses that
allows for a simple connection between particle and spin systems, and that
permits the study of dynamical heterogeneities within a fixed frame of
reference similar to the one used for spin glasses. We apply this framework to
the study of the dynamics of colloidal particle suspensions for packing
fractions corresponding to the supercooled and glassy regimes, which are probed
via confocal microscopy. | cond-mat_dis-nn |
Electronic properties of the 1D Frenkel-Kontorova model: The energy spectra and quantum diffusion of an electron in a 1D
incommensurate Frenkel-Kontorova (FK) model are studied numerically. We found
that the spectral and dynamical properties of electron display quite different
behaviors in invariance circle regime and in Cantorus regime. In the former
case, it is similar to that of the Harper model, whereas in the latter case, it
is similar to that of the Fibonacci model. The relationship between spectral
and transport properties is discussed. | cond-mat_dis-nn |
Dense Hebbian neural networks: a replica symmetric picture of
unsupervised learning: We consider dense, associative neural-networks trained with no supervision
and we investigate their computational capabilities analytically, via a
statistical-mechanics approach, and numerically, via Monte Carlo simulations.
In particular, we obtain a phase diagram summarizing their performance as a
function of the control parameters such as the quality and quantity of the
training dataset and the network storage, valid in the limit of large network
size and structureless datasets. Moreover, we establish a bridge between
macroscopic observables standardly used in statistical mechanics and loss
functions typically used in the machine learning. As technical remarks, from
the analytic side, we implement large deviations and stability analysis within
Guerra's interpolation to tackle the not-Gaussian distributions involved in the
post-synaptic potentials while, from the computational counterpart, we insert
Plefka approximation in the Monte Carlo scheme, to speed up the evaluation of
the synaptic tensors, overall obtaining a novel and broad approach to
investigate neural networks in general. | cond-mat_dis-nn |
Modal makeup of transmission eigenchannels: Transmission eigenchannels and quasi-normal modes are powerful bases for
describing wave transport and controlling transmission and energy storage in
disordered media. Here we elucidate the connection between these approaches by
expressing the transmission matrix (TM) at a particular frequency as a sum of
TMs for individual modes drawn from a broad spectral range. The wide range of
transmission eigenvalues and correlation frequencies of eigenchannels of
transmission is explained by the increasingly off-resonant excitation of modes
contributing to eigenchannels with decreasing transmission and by the phasing
between these contributions. | cond-mat_dis-nn |
A Wavelet Analysis of Transient Spike Trains of Hodgkin-Huxley Neurons: Transient spike trains consisting of $M$ (= 1 - 5) pulses generated by single
Hodgkin-Huxley (HH) neurons, have been analyzed by using both the continuous
and discrete wavelet transformations (WT). We have studied effects of
variations in the interspike intervals (ISI) of the spikes and effects of
noises on the energy distribution and the wavelet entropy, which are expressed
in terms of the WT expansion coefficients. The results obtained by the WT are
discussed in connection with those obtained by the Fourier transformation. | cond-mat_dis-nn |
Study of longitudinal fluctuations of the Sherrington-Kirkpatrick model: We study finite-size corrections to the free energy of the
Sherrington-Kirkpatrick spin glass in the low temperature phase. We investigate
the role of longitudinal fluctuations in these corrections, neglecting the
transverse contribution. In particular, we are interested in the exponent
$\alpha$ defined by the relation $f-f_\infty\sim N^{-\alpha}$. We perform both
an analytical and numerical estimate of the analytical result for $\alpha$.
From both the approaches we get the result: $\alpha=0.8$. | cond-mat_dis-nn |
Thermodynamics of the Lévy spin glass: We investigate the L\'evy glass, a mean-field spin glass model with power-law
distributed couplings characterized by a divergent second moment. By combining
extensively many small couplings with a spare random backbone of strong bonds
the model is intermediate between the Sherrington-Kirkpatrick and the
Viana-Bray model. A truncated version where couplings smaller than some
threshold $\eps$ are neglected can be studied within the cavity method
developed for spin glasses on locally tree-like random graphs. By performing
the limit $\eps\to 0$ in a well-defined way we calculate the thermodynamic
functions within replica symmetry and determine the de Almeida-Thouless line in
the presence of an external magnetic field. Contrary to previous findings we
show that there is no replica-symmetric spin glass phase. Moreover we determine
the leading corrections to the ground-state energy within one-step replica
symmetry breaking. The effects due to the breaking of replica symmetry appear
to be small in accordance with the intuitive picture that a few strong bonds
per spin reduce the degree of frustration in the system. | cond-mat_dis-nn |
Bosons in Disordered Optical Potentials: In this work we systematically investigate the condensate properties,
superfluid properties and quantum phase transitions in interacting Bose gases
trapped in disordered optical potentials. We numerically solve the Bose-Hubbard
Hamiltonian exactly for different: (a) types of disorder, (b) disorder
strengths, and (c) interatomic interactions. The three types of disorder
studied are: quasiperiodic disorder, uniform random disorder and random
speckle-type disorder. We find that the Bose glass, as identified by Fisher et
al [Phys. Rev. B {\bf 40}, 546 (1989)], contains a normal condensate component
and we show how the three different factors listed above affect it. | cond-mat_dis-nn |
Diffusion of a particle in the Gaussian random energy landscape:
Einstein relation and analytical properties of average velocity and
diffusivity as functions of driving force: We demonstrate that the Einstein relation for the diffusion of a particle in
the random energy landscape with the Gaussian density of states is an exclusive
1D property and does not hold in higher dimensions. We also consider the
analytical properties of the particle velocity and diffusivity for the limit of
weak driving force and establish connection between these properties and
dimensionality and spatial correlation of the random energy landscape. | cond-mat_dis-nn |
Interaction-Driven Instabilities in the Random-Field XXZ Chain: Despite enormous efforts devoted to the study of the many-body localization
(MBL) phenomenon, the nature of the high-energy behavior of the Heisenberg spin
chain in a strong random magnetic field is lacking consensus. Here, we take a
step back by exploring the weak interaction limit starting from the Anderson
localized (AL) insulator. Through shift-invert diagonalization, we find that
below a certain disorder threshold $h^*$, weak interactions necessarily lead to
ergodic instability, whereas at strong disorder the AL insulator directly turns
into MBL. This agrees with a simple interpretation of the avalanche theory for
restoration of ergodicity. We further map the phase diagram for the generic XXZ
model in the disorder $h$ -- interaction $\Delta$ plane. Taking advantage of
the total magnetization conservation, our results unveil the remarkable
behavior of the spin-spin correlation functions: in the regime indicated as MBL
by standard observables, their exponential decay undergoes a unique inversion
of orientation $\xi_z>\xi_x$. We find that the longitudinal length $\xi_z$ is a
key quantity for capturing ergodic instabilities, as it increases with system
size near the thermal phase, in sharp contrast to its transverse counterpart
$\xi_x$. | cond-mat_dis-nn |
Statistical properties of localisation--delocalisation transition in one
dimension: We study a one-dimensional model of disordered electrons (also relevant for
random spin chains), which exhibits a delocalisation transition at
half-filling. Exact probability distribution functions for the Wigner time and
transmission coefficient are calculated. We identify and distinguish those
features of probability densities that are due to rare, trapping configurations
of the random potential from those which are due to the proximity to the
delocalisation transition. | cond-mat_dis-nn |
Finite-size scaling with respect to interaction and disorder strength at
the many-body localization transition: We present a finite-size scaling for both interaction and disorder strengths
in the critical regime of the many-body localization (MBL) transition for a
spin-1/2 XXZ spin chain with a random field by studying level statistics. We
show how the dynamical transition from the thermal to MBL phase depends on
interaction together with disorder by evaluating the ratio of adjacent level
spacings, and thus, extend previous studies in which interaction coupling is
fixed. We introduce an extra critical exponent in order to describe the
nontrivial interaction dependence of the MBL transition. It is characterized by
the ratio of the disorder strength to the power of the interaction coupling
with respect to the extra critical exponent and not by the simple ratio between
them. | cond-mat_dis-nn |
Rare regions and avoided quantum criticality in disordered Weyl
semimetals and superconductors: Disorder in Weyl semimetals and superconductors is surprisingly subtle,
attracting attention and competing theories in recent years. In this brief
review, we discuss the current theoretical understanding of the effects of
short-ranged, quenched disorder on the low energy-properties of
three-dimensional, topological Weyl semimetals and superconductors. We focus on
the role of non-perturbative rare region effects on destabilizing the semimetal
phase and rounding the expected semimetal-to-diffusive metal transition into a
cross over. Furthermore, the consequences of disorder on the resulting nature
of excitations, transport, and topology are reviewed. New results on a
bipartite random hopping model are presented that confirm previous results in a
$p+ip$ Weyl superconductor, demonstrating that particle-hole symmetry is
insufficient to help stabilize the Weyl semimetal phase in the presence of
disorder. The nature of the avoided transition in a model for a single Weyl
cone in the continuum is discussed. We close with a discussion of open
questions and future directions. | cond-mat_dis-nn |
One step RSB scheme for the rate distortion function: We apply statistical mechanics to an inverse problem of linear mapping to
investigate the physics of the irreversible compression. We use the replica
symmetry breaking (RSB) technique with a toy model to demonstrate the Shannon's
result. The rate distortion function, which is widely known as the theoretical
limit of the compression with a fidelity criterion, is derived using the Parisi
one step RSB scheme. The bound can not be achieved in the sparsely-connected
systems, where suboptimal solutions dominate the capacity. | cond-mat_dis-nn |
On reducing Terrorism Power: A Hint from Physics: The September 11 attack on the US has revealed an unprecedented terrorism
worldwide range of destruction. Recently, it has been related to the
percolation of worldwide spread passive supporters. This scheme puts the
suppression of the percolation effect as the major strategic issue in the fight
against terrorism. Accordingly the world density of passive supporters should
be reduced below the percolation threshold. In terms of solid policy, it means
to neutralize millions of random passive supporters, which is contrary to
ethics and out of any sound practical scheme. Given this impossibility we
suggest instead a new strategic scheme to act directly on the value of the
terrorism percolation threshold itself without harming the passive supporters.
Accordingly we identify the space hosting the percolation phenomenon to be a
multi-dimensional virtual social space which extends the ground earth surface
to include the various independent terrorist-fighting goals. The associated
percolating cluster is then found to create long-range ground connections to
terrorism activity. We are thus able to modify the percolation threshold pc in
the virtual space to reach p<pc by decreasing the social space dimension,
leaving the density p unchanged. At once that would break down the associated
world terrorism network to a family of unconnected finite size clusters. The
current world terrorism threat would thus shrink immediately and spontaneously
to a local geographic problem. There, military action would become limited and
efficient. | cond-mat_dis-nn |
Finite-size relaxational dynamics of a spike random matrix spherical
model: We present a thorough numerical analysis of the relaxational dynamics of the
Sherrington-Kirkpatrick spherical model with an additive non-disordered
perturbation for large but finite sizes $N$. In the thermodynamic limit and at
low temperatures, the perturbation is responsible for a phase transition from a
spin glass to a ferromagnetic phase. We show that finite size effects induce
the appearance of a distinctive slow regime in the relaxation dynamics, the
extension of which depends on the size of the system and also on the strength
of the non-disordered perturbation. The long time dynamics is characterized by
the two largest eigenvalues of a spike random matrix which defines the model,
and particularly by the statistics of the gap between them. We characterize the
finite size statistics of the two largest eignevalues of the spike random
matrices in the different regimes, sub-critical, critical and super-critical,
confirming some known results and anticipating others, even in the less studied
critical regime. We also numerically characterize the finite size statistics of
the gap, which we hope may encourage analytical work which is lacking. Finally,
we compute the finite size scaling of the long time relaxation of the energy,
showing the existence of power laws with exponents that depend on the strenght
of the non-disordered perturbation, in a way which is governed by the finite
size statistics of the gap. | cond-mat_dis-nn |
Slow oscillating dynamics of a two-level system subject to a fast
telegraph noise: beyond the NIBA approximation: We study the dynamics of a two-site model in which the tunneling amplitude
between the sites is not constant but rather a high-frequency noise. Obviously,
the population imbalance in this model decays exponentially with time.
Remarkably, the decay is modified dramatically when the level asymmetry
fluctuates in-phase with fluctuations of the tunneling amplitude. For
particular type of these in-phase fluctuations, namely, the telegraph noise, we
find the exact solution for the average population dynamics. It appears that
the population imbalance between the sites starting from 1 at time $t=0$
approaches a constant value in the limit $t\rightarrow \infty$. At finite bias,
the imbalance goes to zero at $t\rightarrow \infty$, while the dynamics of the
decay governed by noise acquires an oscillatory character. | cond-mat_dis-nn |
Correlation-induced localization: A new paradigm of Anderson localization caused by correlations in the
long-range hopping along with uncorrelated on-site disorder is considered which
requires a more precise formulation of the basic localization-delocalization
principles. A new class of random Hamiltonians with translation-invariant
hopping integrals is suggested and the localization properties of such models
are established both in the coordinate and in the momentum spaces alongside
with the corresponding level statistics. Duality of translation-invariant
models in the momentum and coordinate space is uncovered and exploited to find
a full localization-delocalization phase diagram for such models. The crucial
role of the spectral properties of hopping matrix is established and a new
matrix inversion trick is suggested to generate a one-parameter family of
equivalent localization/delocalization problems. Optimization over the free
parameter in such a transformation together with the
localization/delocalization principles allows to establish exact bounds for the
localized and ergodic states in long-range hopping models. When applied to the
random matrix models with deterministic power-law hopping this transformation
allows to confirm localization of states at all values of the exponent in
power-law hopping and to prove analytically the symmetry of the exponent in the
power-law localized wave functions. | cond-mat_dis-nn |
Theory of Non-linear Susceptibility and Correlation Length in Glasses
and Liquids: Within the framework of the effective potential theory of the structural
glass transition, we calculate for the p-spin model a static nonlinear
susceptibility related to a four-point density correlation function, and show
that it grows and diverges in mean field with exponent $\gamma=1/2$ as the mode
coupling critical temperature T_c is approached from below. When T_c is
approached from above, we calculate within the mode coupling framework a
dynamic nonlinear susceptibility and show that there is a characteristic time
where the susceptibility is a maximum, and that this time grows with decreasing
T. We find that this susceptibility diverges as T_c is approached from above,
and has key features in common with the ``displacement-displacement
susceptibility'' recently introduced to measure correlated particle motion in
simulations of glass-forming liquids. | cond-mat_dis-nn |
Magetoresistance of RuO_2-based resistance thermometers below 0.3 K: We have determined the magnetoresistance of RuO_2-based resistors (Scientific
Instruments RO-600) between 0.05 K and 0.3 K in magnetic fields up to 8 T. The
magnetoresistance is negative around 0.5 T and then becomes positive at larger
fields. The magnitude of the negative magnetoresistance increases rapidly as
the temperature is lowered, while that of the positive magnetoresistance has
smaller temperature dependence. We have also examined the temperature
dependence of the resistance below 50 mK in zero magnetic field. It is
described in the context of variable-range-hopping conduction down to 15 mK.
Hence, the resistors can be used as thermometers down to at least 15 mK. | cond-mat_dis-nn |
Dipolar Interactions and Origin of Spin Ice in Ising Pyrochlore Magnets: Recent experiments suggest that the Ising pyrochlore magnets ${\rm
Ho_{2}Ti_{2}O_{7}}$ and ${\rm Dy_{2}Ti_{2}O_{7}}$ display qualitative
properties of the spin ice model proposed by Harris {\it et al.} \prl {\bf 79},
2554 (1997). We discuss the dipolar energy scale present in both these
materials and consider how they can display spin ice behavior {\it despite} the
presence of long range interactions. Specifically, we present numerical
simulations and a mean field analysis of pyrochlore Ising systems in the
presence of nearest neighbor exchange and long range dipolar interactions. We
find that two possible phases can occur, a long range ordered antiferromagnetic
one and the other dominated by spin ice features. Our quantitative theory is in
very good agreement with experimental data on both ${\rm Ho_{2}Ti_{2}O_{7}}$
and ${\rm Dy_{2}Ti_{2}O_{7}}$. We suggest that the nearest neighbor exchange in
${\rm Dy_{2}Ti_{2}O_{7}}$ is {\it antiferromagnetic} and that spin ice behavior
is induced by long range dipolar interactions. | cond-mat_dis-nn |
Dynamics at the Many-Body Localization Transition: The isolated one-dimensional Heisenberg model with static random magnetic
fields has become paradigmatic for the analysis of many-body localization.
Here, we study the dynamics of this system initially prepared in a
highly-excited nonstationary state. Our focus is on the probability for finding
the initial state later in time, the so-called survival probability. Two
distinct behaviors are identified before equilibration. At short times, the
decay is very fast and equivalent to that of clean systems. It subsequently
slows down and develops a powerlaw behavior with an exponent that coincides
with the multifractal dimension of the eigenstates. | cond-mat_dis-nn |
How genealogies are affected by the speed of evolution: In a series of recent works it has been shown that a class of simple models
of evolving populations under selection leads to genealogical trees whose
statistics are given by the Bolthausen-Sznitman coalescent rather than by the
well known Kingman coalescent in the case of neutral evolution. Here we show
that when conditioning the genealogies on the speed of evolution, one finds a
one parameter family of tree statistics which interpolates between the
Bolthausen-Sznitman and Kingman's coalescents. This interpolation can be
calculated explicitly for one specific version of the model, the exponential
model. Numerical simulations of another version of the model and a
phenomenological theory indicate that this one-parameter family of tree
statistics could be universal. We compare this tree structure with those
appearing in other contexts, in particular in the mean field theory of spin
glasses. | cond-mat_dis-nn |
Conserved Dynamics and Interface Roughening in Spontaneous Imbibition :
A Phase Field Model: The propagation and roughening of a fluid-gas interface through a disordered
medium in the case of capillary driven spontaneous imbibition is considered.
The system is described by a conserved (model B) phase-field model, with the
structure of the disordered medium appearing as a quenched random field
$\alpha({\bf x})$. The flow of liquid into the medium is obtained by imposing a
non-equilibrium boundary condition on the chemical potential, which reproduces
Washburn's equation $H \sim t^{1/2}$ for the slowing down motion of the average
interface position $H$. The interface is found to be superrough, with global
roughness exponent $\chi \approx 1.25$, indicating anomalous scaling. The
spatial extent of the roughness is determined by a length scale $\xi_{\times}
\sim H^{1/2}$ arising from the conservation law. The interface advances by
avalanche motion, which causes temporal multiscaling and qualitatively
reproduces the experimental results of Horv\a'ath and Stanley [Phys. Rev. E
{\bf 52} 5166 (1995)] on the temporal scaling of the interface. | cond-mat_dis-nn |
More than two equally probable variants of signal in Kauffman networks
as an important overlooked case, negative feedbacks allow life in chaos: There are three main aims of this paper. 1- I explain reasons why I await
life to lie significantly deeper in chaos than Kauffman approach does, however
still in boundary area near `the edge of chaos and order'. The role of negative
feedbacks in stability of living objects is main of those reasons. In
Kauffman's approach regulation using negative feedbacks is not considered
sufficiently, e.g. in gene regulatory model based on Boolean networks, which
indicates therefore not proper source of stability. Large damage avalanche is
available only in chaotic phase. It models death in all living objects
necessary for Darwinian elimination. It is the first step of my approach
leading to structural tendencies which are effects of adaptive evolution of
dynamic complex (maturely chaotic) networks. 2- Introduction of s>=2 equally
probable variants of signal (state of node in Kauffman network) as
interpretively based new statistical mechanism (RSN) instead of the bias p -
probability of one of signal variants used in RBN family and RNS. It is also
different than RWN model. For this mechanism which can be treated as very
frequent, ordered phase occurs only in exceptional cases but for this approach
the chaotic phase is investigated. Annealed approximation expectations and
simulations of damage spreading for different network types (similar to CRBN,
FSRBN and EFRBN but with s>=2) are described. Degree of order in chaotic phase
in dependency of network parameters and type is discussed. By using such order
life evolve. 3- A simplified algorithm called `reversed-annealed' for
statistical simulation of damage spreading is described. It is used for
simulations presented in this and next papers describing my approach. | cond-mat_dis-nn |
Bias driven coherent carrier dynamics in a two-dimensional aperiodic
potential: We study the dynamics of an electron wave-packet in a two-dimensional square
lattice with an aperiodic site potential in the presence of an external uniform
electric field. The aperiodicity is described by $\epsilon_{\bf m} =
V\cos{(\pi\alpha m_x^{\nu_x})}\cos{(\pi\alpha m_y^{\nu_y})}$ at lattice sites
$(m_x, m_y)$, with $\pi \alpha$ being a rational number, and $\nu_x$ and
$\nu_y$ tunable parameters, controlling the aperiodicity. Using an exact
diagonalization procedure and a finite-size scaling analysis, we show that in
the weakly aperiodic regime ($\nu_x,\nu_y < 1$), a phase of extended states
emerges in the center of the band at zero field giving support to a macroscopic
conductivity in the thermodynamic limit. Turning on the field gives rise to
Bloch oscillations of the electron wave-packet. The spectral density of these
oscillations may display a double peak structure signaling the spatial
anisotropy of the potential landscape. The frequency of the oscillations can be
understood using a semi-classical approach. | cond-mat_dis-nn |
Unraveling the nature of carrier mediated ferromagnetism in diluted
magnetic semiconductors: After more than a decade of intensive research in the field of diluted
magnetic semiconductors (DMS), the nature and origin of ferromagnetism,
especially in III-V compounds is still controversial. Many questions and open
issues are under intensive debates. Why after so many years of investigations
Mn doped GaAs remains the candidate with the highest Curie temperature among
the broad family of III-V materials doped with transition metal (TM) impurities
? How can one understand that these temperatures are almost two orders of
magnitude larger than that of hole doped (Zn,Mn)Te or (Cd,Mn)Se? Is there any
intrinsic limitation or is there any hope to reach in the dilute regime room
temperature ferromagnetism? How can one explain the proximity of (Ga,Mn)As to
the metal-insulator transition and the change from
Ruderman-Kittel-Kasuya-Yosida (RKKY) couplings in II-VI compounds to double
exchange type in (Ga,Mn)N? In spite of the great success of density functional
theory based studies to provide accurately the critical temperatures in various
compounds, till very lately a theory that provides a coherent picture and
understanding of the underlying physics was still missing. Recently, within a
minimal model it has been possible to show that among the physical parameters,
the key one is the position of the TM acceptor level. By tuning the value of
that parameter, one is able to explain quantitatively both magnetic and
transport properties in a broad family of DMS. We will see that this minimal
model explains in particular the RKKY nature of the exchange in
(Zn,Mn)Te/(Cd,Mn)Te and the double exchange type in (Ga,Mn)N and simultaneously
the reason why (Ga,Mn)As exhibits the highest critical temperature among both
II-VI and III-V DMS. | cond-mat_dis-nn |
Absorption spectrum of a one-dimensional chain with Frenkel's exciton
under diagonal disorder represented by hyperbolic defects: A method is proposed for calculating the absorption spectrum of a long
one-dimensional closed-into-a-ring chain with Frenkel's exciton under diagonal
disorder. This disorder is represented by the hyperbolic singularities of
atomic fission. These defects are shown to lead to a wing in the exciton zone
of a chain without defects. The form of the wing does not depend on the
relative positions or number of defects and its value is proportional to the
sum of the amplitudes of the defects. The proposed method uses only the
continual approximation. | cond-mat_dis-nn |
Disorder Induced Anomalous Hall Effect in Type-I Weyl Metals: Connection
between the Kubo-Streda Formula in the Spin and Chiral basis: We study the anomalous Hall effect (AHE) in tilted Weyl metals with weak
Gaussian disorder under the Kubo-Streda formalism in this work. To separate the
three different contributions, namely the intrinsic, side jump and skew
scattering contribution, it is usually considered necessary to go to the
eigenstate (chiral) basis of the Kubo-Streda formula. However, it is more
straight-forward to compute the total Hall current in the spin basis. For the
reason, we develop a systematic and transparent scheme to separate the three
different contributions in the spin basis for relativistic systems by building
a one-to-one correspondence between the Feynman diagrams of the different
mechanisms in the chiral basis and the products of the symmetric and
anti-symmetric part of the polarization operator in the spin basis. We obtain
the three contributions of the AHE in tilted Weyl metals by this scheme and
found that the side jump contribution exceeds both the intrinsic and skew
scattering contribution for the low-energy effective Hamiltonian. We compared
the anomalous Hall current obtained from our scheme with the results from the
semi-classical Boltzmann equation approach under the relaxation time
approximation and found that the results from the two approaches agree with
each other in the leading order of the tilting velocity. | cond-mat_dis-nn |
Energy-Efficient and Robust Associative Computing with Electrically
Coupled Dual Pillar Spin-Torque Oscillators: Dynamics of coupled spin-torque oscillators can be exploited for non-Boolean
information processing. However, the feasibility of coupling large number of
STOs with energy-efficiency and sufficient robustness towards
parameter-variation and thermal-noise, may be critical for such computing
applications. In this work, the impacts of parameter-variation and
thermal-noise on two different coupling mechanisms for STOs, namely,
magnetic-coupling and electrical-coupling are analyzed. Magnetic coupling is
simulated using dipolar-field interactions. For electricalcoupling we employed
global RF-injection. In this method, multiple STOs are phase-locked to a common
RF-signal that is injected into the STOs along with the DC bias. Results for
variation and noise analysis indicate that electrical-coupling can be
significantly more robust as compared to magnetic-coupling. For
room-temperature simulations, appreciable phase-lock was retained among tens of
electrically coupled STOs for up to 20% 3s random variations in critical device
parameters. The magnetic-coupling technique however failed to retain locking
beyond ~3% 3s parameter-variations, even for small-size STO clusters with
near-neighborhood connectivity. We propose and analyze Dual-Pillar STO (DP-STO)
for low-power computing using the proposed electrical coupling method. We
observed that DP-STO can better exploit the electrical-coupling technique due
to separation between the biasing RF signal and its own RF output. | cond-mat_dis-nn |
The integrated density of states of the random graph Laplacian: We analyse the density of states of the random graph Laplacian in the
percolating regime. A symmetry argument and knowledge of the density of states
in the nonpercolating regime allows us to isolate the density of states of the
percolating cluster (DSPC) alone, thereby eliminating trivially localised
states due to finite subgraphs. We derive a nonlinear integral equation for the
integrated DSPC and solve it with a population dynamics algorithm. We discuss
the possible existence of a mobility edge and give strong evidence for the
existence of discrete eigenvalues in the whole range of the spectrum. | cond-mat_dis-nn |
Localized Modes in Open One-Dimensional Dissipative Random Systems: We consider, both theoretically and experimentally, the excitation and
detection of the localized quasi-modes (resonances) in an open dissipative 1D
random system. We show that even though the amplitude of transmission drops
dramatically so that it cannot be observed in the presence of small losses,
resonances are still clearly exhibited in reflection. Surprisingly, small
losses essentially improve conditions for the detection of resonances in
reflection as compared with the lossless case. An algorithm is proposed and
tested to retrieve sample parameters and resonances characteristics inside the
random system exclusively from reflection measurements. | cond-mat_dis-nn |
Level spacing distribution of localized phases induced by quasiperiodic
potentials: Level statistics is a crucial tool in the exploration of localization
physics. The level spacing distribution of the disordered localized phase
follows Poisson statistics, and many studies naturally apply it to the
quasiperiodic localized phase. Here we analytically obtain the level spacing
distribution of the quasiperiodic localized phase, and find that it deviates
from Poisson statistics. Moreover, based on this level statistics, we derive
the ratio of adjacent gaps and find that for a single sample, it is a $\delta$
function, which is in excellent agreement with numerical studies. Additionally,
unlike disordered systems, in quasiperiodic systems, there are variations in
the level spacing distribution across different regions of the spectrum, and
increasing the size and increasing the sample are non-equivalent. Our findings
carry significant implications for the reevaluation of level statistics in
quasiperiodic systems and a profound understanding of the distinct effects of
quasiperiodic potentials and disorder induced localization. | cond-mat_dis-nn |
Geometry, Topology and Simplicial Synchronization: Simplicial synchronization reveals the role that topology and geometry have
in determining the dynamical properties of simplicial complexes. Simplicial
network geometry and topology are naturally encoded in the spectral properties
of the graph Laplacian and of the higher-order Laplacians of simplicial
complexes. Here we show how the geometry of simplicial complexes induces
spectral dimensions of the simplicial complex Laplacians that are responsible
for changing the phase diagram of the Kuramoto model. In particular, simplicial
complexes displaying a non-trivial simplicial network geometry cannot sustain a
synchronized state in the infinite network limit if their spectral dimension is
smaller or equal to four. This theoretical result is here verified on the
Network Geometry with Flavor simplicial complex generative model displaying
emergent hyperbolic geometry. On its turn simplicial topology is shown to
determine the dynamical properties of the higher-order Kuramoto model. The
higher-orderKuramoto model describes synchronization of topological signals,
i.e. phases not only associated to the nodes of a simplicial complexes but
associated also to higher-order simplices, including links, triangles and so
on. This model displays discontinuous synchronization transitions when
topological signals of different dimension and/or their solenoidal and
irrotational projections are coupled in an adaptive way. | cond-mat_dis-nn |
Many-Body Localization: Transitions in Spin Models: We study the transitions between ergodic and many-body localized phases in
spin systems, subject to quenched disorder, including the Heisenberg chain and
the central spin model. In both cases systems with common spin lengths $1/2$
and $1$ are investigated via exact numerical diagonalization and random matrix
techniques.
Particular attention is paid to the sample-to-sample variance $(\Delta_sr)^2$
of the averaged consecutive-gap ratio $\langle r\rangle$ for different disorder
realizations. For both types of systems and spin lengths we find a maximum in
$\Delta_sr$ as a function of disorder strength, accompanied by an inflection
point of $\langle r\rangle$, signaling the transition from ergodicity to
many-body localization. The critical disorder strength is found to be somewhat
smaller than the values reported in the recent literature.
Further information about the transitions can be gained from the probability
distribution of expectation values within a given disorder realization. | cond-mat_dis-nn |
Full solution for the storage of correlated memories in an
autoassociative memory: We complement our previous work [arxiv: 0707.0565] with the full (non
diluted) solution describing the stable states of an attractor network that
stores correlated patterns of activity. The new solution provides a good fit of
simulations of a network storing the feature norms of McRae and colleagues
[McRae et al, 2005], experimentally obtained combinations of features
representing concepts in semantic memory. We discuss three ways to improve the
storage capacity of the network: adding uninformative neurons, removing
informative neurons and introducing popularity-modulated hebbian learning. We
show that if the strength of synapses is modulated by an exponential decay of
the popularity of the pre-synaptic neuron, any distribution of patterns can be
stored and retrieved with approximately an optimal storage capacity - i.e, C ~
I.p, the minimum number of connections per neuron needed to sustain the
retrieval of a pattern is proportional to the information content of the
pattern multiplied by the number of patterns stored in the network. | cond-mat_dis-nn |
Generic Modeling of Chemotactic Based Self-Wiring of Neural Networks: The proper functioning of the nervous system depends critically on the
intricate network of synaptic connections that are generated during the system
development. During the network formation, the growth cones migrate through the
embryonic environment to their targets using chemical communication. A major
obstacle in the elucidation of fundamental principles underlying this
self-wiring is the complexity of the system being analyzed. Hence much effort
is devoted to in-vitro experiments of simpler 2D model systems. In these
experiments neurons are placed on Poly-L-Lysine (PLL) surfaces so it is easier
to monitor their self-wiring. We developed a model to reproduce the salient
features of the 2D systems, inspired by the study of bacterial colony's growth
and the aggregation of amoebae. We represent the neurons (each composed of
cell's soma, neurites and growth cones) by active elements that capture the
generic features of the real neurons. The model also incorporates stationary
units representing the cells' soma and communicating walkers representing the
growth cones. The stationary units send neurites one at a time, and respond to
chemical signaling. The walkers migrate in response to chemotaxis substances
emitted by the soma and communicate with each other and with the soma by means
of chemotactic ``feedback''. The interplay between the chemo-repulsive and
chemo-attractive responses is determined by the dynamics of the walker's
internal energy which is controlled by the soma. These features enable the
neurons to perform the complex task of self-wiring. | cond-mat_dis-nn |
Surface properties at the Kosterlitz-Thouless transition: Monte Carlo simulations of the two-dimensional XY model are performed in a
square geometry with free and mixed fixed-free boundary conditions. Using a
Schwarz-Christoffel conformal mapping, we deduce the exponent eta of the order
parameter correlation function and its surface equivalent eta_parallel at the
Kosterlitz-Thouless transition temperature. The well known value eta(T_{KT}) =
1/4 is easily recovered even with systems of relatively small sizes, since the
shape effects are encoded in the conformal mapping. The exponent associated to
the surface correlations is similarly obtained eta_1(T_{KT}) ~= 0.54. | cond-mat_dis-nn |
Application of Polynomial Algorithms to a Random Elastic Medium: A randomly pinned elastic medium in two dimensions is modeled by a disordered
fully-packed loop model. The energetics of disorder-induced dislocations is
studied using exact and polynomial algorithms from combinatorial optimization.
Dislocations are found to become unbound at large scale, and the elastic phase
is thus unstable giving evidence for the absence of a Bragg glass in two
dimensions. | cond-mat_dis-nn |
Broken Replica Symmetry Bounds in the Mean Field Spin Glass Model: By using a simple interpolation argument, in previous work we have proven the
existence of the thermodynamic limit, for mean field disordered models,
including the Sherrington-Kirkpatrick model, and the Derrida p-spin model. Here
we extend this argument in order to compare the limiting free energy with the
expression given by the Parisi Ansatz, and including full spontaneous replica
symmetry breaking. Our main result is that the quenched average of the free
energy is bounded from below by the value given in the Parisi Ansatz uniformly
in the size of the system. Moreover, the difference between the two expressions
is given in the form of a sum rule, extending our previous work on the
comparison between the true free energy and its replica symmetric
Sherrington-Kirkpatrick approximation. We give also a variational bound for the
infinite volume limit of the ground state energy per site. | cond-mat_dis-nn |
Quantized Repetitions of the Cuprate Pseudogap Line: The cuprate superconductors display several characteristic temperatures which
decrease as the material composition is doped, tracing lines across the
temperature-doping phase diagram. Foremost among these is the pseudogap
transition. At a higher temperature a peak is seen in the magnetic
susceptibility, and changes in symmetry and in transport are seen at other
characteristic temperatures. We report a meta-analysis of all measurements of
characteristic temperatures well above $T_c$ in strontium doped lanthanum
cuprate (LSCO) and oxygen doped YBCO. The experimental corpus shows that the
pseudogap line is one of a family of four straight lines which stretches across
the phase diagram from low to high doping, and from $T_c$ up to $700$ K. These
lines all originate from a single point near the overdoped limit of the
superconducting phase and increase as doping is reduced. The slope of the
pseudogap lines is quantized, with the second, third, and fourth lines having
slopes that are respectively $1/2,\;1/3,$ and $1/4$ of the slope of the highest
line. This pattern suggests that the cuprates host a single mother phase
controlled by a 2-D sheet density which is largest at zero doping and which
decreases linearly with hole density, and that the pseudogap lines, charge
density wave order, and superconductivity are all subsidiary effects supported
by the mother phase. | cond-mat_dis-nn |
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