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Anomalous Skin Effects in Disordered Systems with a Single non-Hermitian
Impurity: We explore anomalous skin effects at non-Hermitian impurities by studying
their interplay with potential disorder and by exactly solving a minimal
lattice model. A striking feature of the solvable single-impurity model is that
the presence of anisotropic hopping terms can induce a scale-free accumulation
of all eigenstates opposite to the bulk hopping direction, although the
nonmonotonic behavior is fine tuned and further increasing such hopping weakens
and eventually reverses the effect. The interplay with bulk potential disorder,
however, qualitatively enriches this phenomenology leading to a robust
nonmonotonic localization behavior as directional hopping strengths are tuned.
Nonmonotonicity persists even in the limit of an entirely Hermitian bulk with a
single non-Hermitian impurity. | cond-mat_dis-nn |
Distribution of critical temperature at Anderson localization: Based on a local mean-field theory approach at Anderson localization, we find
a distribution function of critical temperature from that of disorder. An
essential point of this local mean-field theory approach is that the
information of the wave-function multifractality is introduced. The
distribution function of the Kondo temperature ($T_{K}$) shows a power-law tail
in the limit of $T_{K} \rightarrow 0$ regardless of the Kondo coupling
constant. We also find that the distribution function of the ferromagnetic
transition temperature ($T_{c}$) gives a power-law behavior in the limit of
$T_{c} \rightarrow 0$ when an interaction parameter for ferromagnetic
instability lies below a critical value. However, the $T_{c}$ distribution
function stops the power-law increasing behavior in the $T_{c} \rightarrow 0$
limit and vanishes beyond the critical interaction parameter inside the
ferromagnetic phase. These results imply that the typical Kondo temperature
given by a geometric average always vanishes due to finite density of the
distribution function in the $T_{K} \rightarrow 0$ limit while the typical
ferromagnetic transition temperature shows a phase transition at the critical
interaction parameter. We propose that the typical transition temperature
serves a criterion for quantum Griffiths phenomena vs. smeared transitions:
Quantum Griffiths phenomena occur above the typical value of the critical
temperature while smeared phase transitions result at low temperatures below
the typical transition temperature. We speculate that the ferromagnetic
transition at Anderson localization shows the evolution from quantum Griffiths
phenomena to smeared transitions around the critical interaction parameter at
low temperatures. | cond-mat_dis-nn |
Neural network enhanced hybrid quantum many-body dynamical distributions: Computing dynamical distributions in quantum many-body systems represents one
of the paradigmatic open problems in theoretical condensed matter physics.
Despite the existence of different techniques both in real-time and frequency
space, computational limitations often dramatically constrain the physical
regimes in which quantum many-body dynamics can be efficiently solved. Here we
show that the combination of machine learning methods and complementary
many-body tensor network techniques substantially decreases the computational
cost of quantum many-body dynamics. We demonstrate that combining kernel
polynomial techniques and real-time evolution, together with deep neural
networks, allows to compute dynamical quantities faithfully. Focusing on
many-body dynamical distributions, we show that this hybrid neural-network
many-body algorithm, trained with single-particle data only, can efficiently
extrapolate dynamics for many-body systems without prior knowledge.
Importantly, this algorithm is shown to be substantially resilient to numerical
noise, a feature of major importance when using this algorithm together with
noisy many-body methods. Ultimately, our results provide a starting point
towards neural-network powered algorithms to support a variety of quantum
many-body dynamical methods, that could potentially solve computationally
expensive many-body systems in a more efficient manner. | cond-mat_dis-nn |
Microscopic theory of OMAR based on kinetic equations for quantum spin
correlations: The correlation kinetic equation approach is developed that allows describing
spin correlations in a material with hopping transport. The quantum nature of
spin is taken into account. The approach is applied to the problem of the
bipolaron mechanism of organic magnetoresistance (OMAR) in the limit of large
Hubbard energy and small applied electric field. The spin relaxation that is
important to magnetoresistance is considered to be due to hyperfine interaction
with atomic nuclei. It is shown that the lineshape of magnetoresistance depends
on short-range transport properties. Different model systems with identical
hyperfine interaction but different statistics of electron hops lead to
different lineshapes of magnetoresistance including the two empirical laws
$H^2/(H^2 + H_0^2)$ and $H^2/(|H| + H_0)^2$ that are commonly used to fit
experimental results. | cond-mat_dis-nn |
Functional Renormalization for Disordered Systems, Basic Recipes and
Gourmet Dishes: We give a pedagogical introduction into the functional renormalization group
treatment of disordered systems. After a review of its phenomenology, we show
why in the context of disordered systems a functional renormalization group
treatment is necessary, contrary to pure systems, where renormalization of a
single coupling constant is sufficient. This leads to a disorder distribution,
which after a finite renormalization becomes non-analytic, thus overcoming the
predictions of the seemingly exact dimensional reduction. We discuss, how the
non-analyticity can be measured in a simulation or experiment. We then
construct a renormalizable field theory beyond leading order. We discuss an
elastic manifold embedded in N dimensions, and give the exact solution for N to
infinity. This is compared to predictions of the Gaussian replica variational
ansatz, using replica symmetry breaking. We further consider random field
magnets, and supersymmetry. We finally discuss depinning, both isotropic and
anisotropic, and universal scaling function. | cond-mat_dis-nn |
"Burning and sticking" model for a porous material: suppression of the
topological phase transition due to the backbone reinforcement effect: We introduce and study the "burning-and-sticking" (BS) lattice model for the
porous material that involves sticking of emerging finite clusters to the
mainland. In contrast with other single-cluster models, it does not demonstrate
any phase transition: the backbone exists at arbitrarily low concentrations.
The same is true for hybrid models, where the sticking events occur with
probability $q$: the backbone survives at arbitrarily low $q$. Disappearance of
the phase transition is attributed to the backbone reinforcement effect,
generic for models with sticking. A relation between BS and the cluster-cluster
aggregation is briefly discussed. | cond-mat_dis-nn |
Random elastic networks : strong disorder renormalization approach: For arbitrary networks of random masses connected by random springs, we
define a general strong disorder real-space renormalization (RG) approach that
generalizes the procedures introduced previously by Hastings [Phys. Rev. Lett.
90, 148702 (2003)] and by Amir, Oreg and Imry [Phys. Rev. Lett. 105, 070601
(2010)] respectively. The principle is to eliminate iteratively the elementary
oscillating mode of highest frequency associated with either a mass or a spring
constant. To explain the accuracy of the strong disorder RG rules, we compare
with the Aoki RG rules that are exact at fixed frequency. | cond-mat_dis-nn |
Dynamics of disordered elastic systems: We review in these notes some dynamical properties of interfaces in random
media submitted to an external force. We focuss in particular to the response
to a very small force (so called creep motion) and discuss various theoretical
aspects of this problem. We consider in details in particular the case of a one
dimensional interface (domain wall). | cond-mat_dis-nn |
A Theory for Spin Glass Phenomena in Interacting Nanoparticle Systems: Dilute magnetic nanoparticle systems exhibit slow dynamics [1] due to a broad
distribution of relaxation times that can be traced to a correspondingly broad
distribution of particle sizes [1]. However, at higher concentrations
interparticle interactions lead to a slow dynamics that is qualitatively
indistinguishable from that dislayed by atomic spin glasses. A theory is
derived below that accounts quantitatively for the spin-glass behaviour. The
theory predicts that if the interactions become too strong the spin glass
behaviour disappears. This conclusion is in agreement with preliminary
experimental results. | cond-mat_dis-nn |
Fluctuations of random matrix products and 1D Dirac equation with random
mass: We study the fluctuations of certain random matrix products $\Pi_N=M_N\cdots
M_2M_1$ of $\mathrm{SL}(2,\mathbb{R})$, describing localisation properties of
the one-dimensional Dirac equation with random mass. In the continuum limit,
i.e. when matrices $M_n$'s are close to the identity matrix, we obtain
convenient integral representations for the variance
$\Gamma_2=\lim_{N\to\infty}\mathrm{Var}(\ln||\Pi_N||)/N$. The case studied
exhibits a saturation of the variance at low energy $\varepsilon$ along with a
vanishing Lyapunov exponent $\Gamma_1=\lim_{N\to\infty}\ln||\Pi_N||/N$, leading
to the behaviour $\Gamma_2/\Gamma_1\sim\ln(1/|\varepsilon|)\to\infty$ as
$\varepsilon\to0$. Our continuum description sheds new light on the
Kappus-Wegner (band center) anomaly. | cond-mat_dis-nn |
Strong Disorder RG approach - a short review of recent developments: The Strong Disorder RG approach for random systems has been extended in many
new directions since our previous review of 2005 [Phys. Rep. 412, 277]. The aim
of the present colloquium paper is thus to give an overview of these various
recent developments. In the field of quantum disordered models, recent progress
concern Infinite Disorder Fixed Points for short-ranged models in higher
dimensions $d>1$, Strong Disorder Fixed Points for long-ranged models, scaling
of the entanglement entropy in critical ground-states and after quantum
quenches, the RSRG-X procedure to construct the whole set excited stated and
the RSRG-t procedure for the unitary dynamics in Many-Body-Localized Phases,
the Floquet dynamics of periodically driven chains, the dissipative effects
induced by the coupling to external baths, and Anderson Localization models. In
the field of classical disordered models, new applications include the contact
process for epidemic spreading, the strong disorder renormalization procedure
for general master equations, the localization properties of random elastic
networks and the synchronization of interacting non-linear dissipative
oscillators. | cond-mat_dis-nn |
Algorithms for 3D rigidity analysis and a first order percolation
transition: A fast computer algorithm, the pebble game, has been used successfully to
study rigidity percolation on 2D elastic networks, as well as on a special
class of 3D networks, the bond-bending networks. Application of the pebble game
approach to general 3D networks has been hindered by the fact that the
underlying mathematical theory is, strictly speaking, invalid in this case. We
construct an approximate pebble game algorithm for general 3D networks, as well
as a slower but exact algorithm, the relaxation algorithm, that we use for
testing the new pebble game. Based on the results of these tests and additional
considerations, we argue that in the particular case of randomly diluted
central-force networks on BCC and FCC lattices, the pebble game is essentially
exact. Using the pebble game, we observe an extremely sharp jump in the largest
rigid cluster size in bond-diluted central-force networks in 3D, with the
percolating cluster appearing and taking up most of the network after a single
bond addition. This strongly suggests a first order rigidity percolation
transition, which is in contrast to the second order transitions found
previously for the 2D central-force and 3D bond-bending networks. While a first
order rigidity transition has been observed for Bethe lattices and networks
with ``chemical order'', this is the first time it has been seen for a regular
randomly diluted network. In the case of site dilution, the transition is also
first order for BCC, but results for FCC suggest a second order transition.
Even in bond-diluted lattices, while the transition appears massively first
order in the order parameter (the percolating cluster size), it is continuous
in the elastic moduli. This, and the apparent non-universality, make this phase
transition highly unusual. | cond-mat_dis-nn |
Constructing local integrals of motion in the many-body localized phase: Many-body localization provides a generic mechanism of ergodicity breaking in
quantum systems. In contrast to conventional ergodic systems, many-body
localized (MBL) systems are characterized by extensively many local integrals
of motion (LIOM), which underlie the absence of transport and thermalization in
these systems. Here we report a physically motivated construction of local
integrals of motion in the MBL phase. We show that any local operator (e.g., a
local particle number or a spin flip operator), evolved with the system's
Hamiltonian and averaged over time, becomes a LIOM in the MBL phase. Such
operators have a clear physical meaning, describing the response of the MBL
system to a local perturbation. In particular, when a local operator represents
a density of some globally conserved quantity, the corresponding LIOM describes
how this conserved quantity propagates through the MBL phase. Being uniquely
defined and experimentally measurable, these LIOMs provide a natural tool for
characterizing the properties of the MBL phase, both in experiments and
numerical simulations. We demonstrate the latter by numerically constructing an
extensive set of LIOMs in the MBL phase of a disordered spin chain model. We
show that the resulting LIOMs are quasi-local, and use their decay to extract
the localization length and establish the location of the transition between
the MBL and ergodic phases. | cond-mat_dis-nn |
Viscosity and relaxation processes of the liquid become amorphous
Al-Ni-REM alloys: The temperature and time dependencies of viscosity of the liquid alloys,
Al87Ni8Y5, Al86Ni8La6, Al86Ni8Ce6, and the binary Al-Ni and Al-Y melts with Al
concentration over 90 at.% have been studied. Non-monotonic relaxation
processes caused by destruction of nonequilibrium state inherited from the
basic-heterogeneous alloy have been found to take place in Al-Y, Al-Ni-REM
melts after the phase solid-liquid transition. The mechanism of nonmonotonic
relaxation in non-equilibrium melts has been suggested. | cond-mat_dis-nn |
Electric field control of magnetic properties and magneto-transport in
composite multiferroics: We study magnetic state and electron transport properties of composite
multiferroic system consisting of a granular ferromagnetic thin film placed
above the ferroelectric substrate. Ferroelectricity and magnetism in this case
are coupled by the long-range Coulomb interaction. We show that magnetic state
and magneto-transport strongly depend on temperature, external electric field,
and electric polarization of the substrate. Ferromagnetic order exists at
finite temperature range around ferroelectric Curie point. Outside the region
the film is in the superparamagnetic state. We demonstrate that magnetic phase
transition can be driven by an electric field and magneto-resistance effect has
two maxima associated with two magnetic phase transitions appearing in the
vicinity of the ferroelectric phase transition. We show that positions of these
maxima can be shifted by the external electric field and that the magnitude of
the magneto-resistance effect depends on the mutual orientation of external
electric field and polarization of the substrate. | cond-mat_dis-nn |
Near-field EM wave scattering from random self-affine fractal metal
surfaces: spectral dependence of local field enhancements and their
statistics in connection with SERS: By means of rigorous numerical simulation calculations based on the Green's
theorem integral equation formulation, we study the near EM field in the
vicinity of very rough, one-dimensional self-affine fractal surfaces of Ag, Au,
and Cu (for both vacuum and water propagating media) illuminated by a p
polarized field. Strongly localized enhanced optical excitations (hot spots)
are found, with electric field intensity enhancements of close to 4 orders of
magnitude the incident one, and widths below a tenth of the incoming
wavelength. These effects are produced by roughness-induced surface-plasmon
polariton excitation. We study the characteristics of these optical excitations
as well as other properties of the surface electromagnetic field, such as its
statistics (probability density function, average and fluctuations), and their
dependence on the excitation spectrum (in the visible and near infrared). Our
study is relevant to the use of such self-affine fractals as surface-enhanced
Raman scattering substrates, where large local and average field enhancements
are desired. | cond-mat_dis-nn |
Magnitoelastic interaction and long-range magnetic ordering in
two-dimesional ferromagnetics: The influence of magnitoelastic (ME) interaction on the stabilization of
long-range magnetic order (LMO) in the two-dimensional easy-plane ferromagnetic
is investigated in this work. The account of ME exchange results in the root
dispersion law of magnons and appearance of ME gap in the spectra of elementary
excitations. Such a behavior of the spectra testifies to the stabilization of
LMO and finite Curie's temperature. | cond-mat_dis-nn |
Momentum Signatures of Site Percolation in Disordered 2D Ferromagnets: In this work, we consider a two-dimensional square lattice of pinned magnetic
spins with nearest-neighbour interactions and we randomly replace a fixed
proportion of spins with nonmagnetic defects carrying no spin. We focus on the
linear spin-wave regime and address the propagation of a spin-wave excitation
with initial momentum $k_0$. We compute the disorder-averaged momentum
distribution obtained at time $t$ and show that the system exhibits two
regimes. At low defect density, typical disorder configurations only involve a
single percolating magnetic cluster interspersed with single defects
essentially and the physics is driven by Anderson localization. In this case,
the momentum distribution features the emergence of two known emblematic
signatures of coherent transport, namely the coherent backscattering (CBS) peak
located at $-k_0$ and the coherent forward scattering (CFS) peak located at
$k_0$. At long times, the momentum distribution becomes stationary. However,
when increasing the defect density, site percolation starts to set in and
typical disorder configurations display more and more disconnected clusters of
different sizes and shapes. At the same time, the CFS peak starts to oscillate
in time with well defined frequencies. These oscillation frequencies represent
eigenenergy differences in the regular, disorder-immune, part of the
Hamiltonian spectrum. This regular spectrum originates from the small-size
magnetic clusters and its weight grows as the system undergoes site percolation
and small clusters proliferate. Our system offers a unique spectroscopic
signature of cluster formation in site percolation problems. | cond-mat_dis-nn |
Bond-disordered spin systems: Theory and application to doped high-Tc
compounds: We examine the stability of magnetic order in a classical Heisenberg model
with quenched random exchange couplings. This system represents the spin
degrees of freedom in high-$T_\textrm{c}$ compounds with immobile dopants.
Starting from a replica representation of the nonlinear $\sigma$-model, we
perform a renormalization-group analysis. The importance of cumulants of the
disorder distribution to arbitrarily high orders necessitates a functional
renormalization scheme. From the renormalization flow equations we determine
the magnetic correlation length numerically as a function of the impurity
concentration and of temperature. From our analysis follows that
two-dimensional layers can be magnetically ordered for arbitrarily strong but
sufficiently diluted defects. We further consider the dimensional crossover in
a stack of weakly coupled layers. The resulting phase diagram is compared with
experimental data for La$_{2-x}$Sr$_x$CuO$_4$. | cond-mat_dis-nn |
Photonic structures with disorder immunity: Periodic and disordered media are known to possess different transport
properties, either classically or quantum-mechanically. This has been exhibited
by effects such as Anderson localization in systems with disorder and the
existence of photonic bandgaps in the periodic case. In this paper we analyze
the transport properties of disordered waveguides with corners at very low
frequencies, finding that the spectrum, conductance and wavefunctions are
immune to disorder. Our waveguides are constructed by means of randomly
oriented straight segments and connected by corners at right angles. Taking
advantage of a trapping effect that manifests in the corner of a bent
waveguide, we can show that a tight-binding approximation describes the system
reasonably well for any degree of disorder. This provides a wide set of
non-periodic geometries that preserve all the interesting transport properties
of periodic media. | cond-mat_dis-nn |
Absence of Conventional Spin-Glass Transition in the Ising Dipolar
System LiHo_xY_{1-x}F_4: The magnetic properties of single crystals of LiHo_xY_{1-x}F_4 with x=16.5%
and x=4.5% were recorded down to 35 mK using a micro-SQUID magnetometer. While
this system is considered as the archetypal quantum spin glass, the detailed
analysis of our magnetization data indicates the absence of a phase transition,
not only in a transverse applied magnetic field, but also without field. A
zero-Kelvin phase transition is also unlikely, as the magnetization seems to
follow a non-critical exponential dependence on the temperature. Our analysis
thus unmasks the true, short-ranged nature of the magnetic properties of the
LiHo_xY_{1-x}F_4 system, validating recent theoretical investigations
suggesting the lack of phase transition in this system. | cond-mat_dis-nn |
Distribution of the reflection eigenvalues of a weakly absorbing chaotic
cavity: The scattering-matrix product SS+ of a weakly absorbing medium is related by
a unitary transformation to the time-delay matrix without absorption. It
follows from this relationship that the eigenvalues of SS+ for a weakly
absorbing chaotic cavity are distributed according to a generalized Laguerre
ensemble. | cond-mat_dis-nn |
Dynamics of strongly interacting systems: From Fock-space fragmentation
to Many-Body Localization: We study the $t{-}V$ disordered spinless fermionic chain in the strong
coupling regime, $t/V\rightarrow 0$. Strong interactions highly hinder the
dynamics of the model, fragmenting its Hilbert space into exponentially many
blocks in system size. Macroscopically, these blocks can be characterized by
the number of new degrees of freedom, which we refer to as movers. We focus on
two limiting cases: Blocks with only one mover and the ones with a finite
density of movers. The former many-particle block can be exactly mapped to a
single-particle Anderson model with correlated disorder in one dimension. As a
result, these eigenstates are always localized for any finite amount of
disorder. The blocks with a finite density of movers, on the other side, show
an MBL transition that is tuned by the disorder strength. Moreover, we provide
numerical evidence that its ergodic phase is diffusive at weak disorder.
Approaching the MBL transition, we observe sub-diffusive dynamics at finite
time scales and find indications that this might be only a transient behavior
before crossing over to diffusion. | cond-mat_dis-nn |
Hidden Quasicrystal in Hofstadter Butterfly: Topological description of hierarchical sets of spectral gaps of Hofstadter
butterfly is found to be encoded in a quasicrystal where magnetic flux plays
the role of a phase factor that shifts the origin of the quasiperiodic order.
Revealing an intrinsic frustration at smallest energy scale, described by
$\zeta=2-\sqrt{3}$, this irrational number characterizes the universal
butterfly and is related to two quantum numbers that includes the Chern number
of quantum Hall states. With a periodic drive that induces phase transitions in
the system, the fine structure of the butterfly is shown to be amplified making
states with large topological invariants accessible experimentally . | cond-mat_dis-nn |
Thermodynamics of spin systems on small-world hypergraphs: We study the thermodynamic properties of spin systems on small-world
hypergraphs, obtained by superimposing sparse Poisson random graphs with p-spin
interactions onto a one-dimensional Ising chain with nearest-neighbor
interactions. We use replica-symmetric transfer-matrix techniques to derive a
set of fixed-point equations describing the relevant order parameters and free
energy, and solve them employing population dynamics. In the special case where
the number of connections per site is of the order of the system size we are
able to solve the model analytically. In the more general case where the number
of connections is finite we determine the static and dynamic
ferromagnetic-paramagnetic transitions using population dynamics. The results
are tested against Monte-Carlo simulations. | cond-mat_dis-nn |
Weighted evolving networks: coupling topology and weights dynamics: We propose a model for the growth of weighted networks that couples the
establishment of new edges and vertices and the weights' dynamical evolution.
The model is based on a simple weight-driven dynamics and generates networks
exhibiting the statistical properties observed in several real-world systems.
In particular, the model yields a non-trivial time evolution of vertices'
properties and scale-free behavior for the weight, strength and degree
distributions. | cond-mat_dis-nn |
Thermodynamic signature of growing amorphous order in glass-forming
liquids: Although several theories relate the steep slowdown of glass formers to
increasing spatial correlations of some sort, standard static correlation
functions show no evidence for this. We present results that reveal for the
first time a qualitative thermodynamic difference between the high temperature
and deeply supercooled equilibrium glass-forming liquid: the influence of
boundary conditions propagates into the bulk over larger and larger
lengthscales upon cooling, and, as this static correlation length grows, the
influence decays nonexponentially. Increasingly long-range susceptibility to
boundary conditions is expected within the random firt-order theory (RFOT) of
the glass transition, but a quantitative account of our numerical results
requires a generalization of RFOT where the surface tension between states
fluctuates. | cond-mat_dis-nn |
"Single Ring Theorem" and the Disk-Annulus Phase Transition: Recently, an analytic method was developed to study in the large $N$ limit
non-hermitean random matrices that are drawn from a large class of circularly
symmetric non-Gaussian probability distributions, thus extending the existing
Gaussian non-hermitean literature. One obtains an explicit algebraic equation
for the integrated density of eigenvalues from which the Green's function and
averaged density of eigenvalues could be calculated in a simple manner. Thus,
that formalism may be thought of as the non-hermitean analog of the method due
to Br\'ezin, Itzykson, Parisi and Zuber for analyzing hermitean non-Gaussian
random matrices. A somewhat surprising result is the so called "Single Ring"
theorem, namely, that the domain of the eigenvalue distribution in the complex
plane is either a disk or an annulus. In this paper we extend previous results
and provide simple new explicit expressions for the radii of the eigenvalue
distiobution and for the value of the eigenvalue density at the edges of the
eigenvalue distribution of the non-hermitean matrix in terms of moments of the
eigenvalue distribution of the associated hermitean matrix. We then present
several numerical verifications of the previously obtained analytic results for
the quartic ensemble and its phase transition from a disk shaped eigenvalue
distribution to an annular distribution. Finally, we demonstrate numerically
the "Single Ring" theorem for the sextic potential, namely, the potential of
lowest degree for which the "Single Ring" theorem has non-trivial consequences. | cond-mat_dis-nn |
Spin-glass behavior in the random-anisotropy Heisenberg model: We perform Monte Carlo simulations in a random anisotropy magnet at a
intermediate exchange to anisotropy ratio. We focus on the out of equilibrium
relaxation after a sudden quenching in the low temperature phase, well below
the freezing one. By analyzing both the aging dynamics and the violation of the
Fluctuation Dissipation relation we found strong evidence of a spin--glass like
behavior. In fact, our results are qualitatively similar to those
experimentally obtained recently in a Heisenberg-like real spin glass. | cond-mat_dis-nn |
Quantum dynamics in canonical and micro-canonical ensembles. Part I.
Anderson localization of electrons: The new numerical approach for consideration of quantum dynamics and
calculations of the average values of quantum operators and time correlation
functions in the Wigner representation of quantum statistical mechanics has
been developed. The time correlation functions have been presented in the form
of the integral of the Weyl's symbol of considered operators and the Fourier
transform of the product of matrix elements of the dynamic propagators. For the
last function the integral Wigner- Liouville's type equation has been derived.
The numerical procedure for solving this equation combining both molecular
dynamics and Monte Carlo methods has been developed. For electrons in
disordered systems of scatterers the numerical results have been obtained for
series of the average values of the quantum operators including position and
momentum dispersions, average energy, energy distribution function as well as
for the frequency dependencies of tensor of electron conductivity and
permittivity according to quantum Kubo formula. Zero or very small value of
static conductivity have been considered as the manifestation of Anderson
localization of electrons in 1D case. Independent evidence of Anderson
localization comes from the behaviour of the calculated time dependence of
position dispersion. | cond-mat_dis-nn |
On Renyi entropies characterizing the shape and the extension of the
phase space representation of quantum wave functions in disordered systems: We discuss some properties of the generalized entropies, called Renyi
entropies and their application to the case of continuous distributions. In
particular it is shown that these measures of complexity can be divergent,
however, their differences are free from these divergences thus enabling them
to be good candidates for the description of the extension and the shape of
continuous distributions. We apply this formalism to the projection of wave
functions onto the coherent state basis, i.e. to the Husimi representation. We
also show how the localization properties of the Husimi distribution on average
can be reconstructed from its marginal distributions that are calculated in
position and momentum space in the case when the phase space has no structure,
i.e. no classical limit can be defined. Numerical simulations on a one
dimensional disordered system corroborate our expectations. | cond-mat_dis-nn |
Phase ordering on small-world networks with nearest-neighbor edges: We investigate global phase coherence in a system of coupled oscillators on a
small-world networks constructed from a ring with nearest-neighbor edges. The
effects of both thermal noise and quenched randomness on phase ordering are
examined and compared with the global coherence in the corresponding \xy model
without quenched randomness. It is found that in the appropriate regime phase
ordering emerges at finite temperatures, even for a tiny fraction of shortcuts.
Nature of the phase transition is also discussed. | cond-mat_dis-nn |
On the formal equivalence of the TAP and thermodynamic methods in the SK
model: We revisit two classic Thouless-Anderson-Palmer (TAP) studies of the
Sherrington-Kirkpatrick model [Bray A J and Moore M A 1980 J. Phys. C 13, L469;
De Dominicis C and Young A P, 1983 J. Phys. A 16, 2063]. By using the
Becchi-Rouet-Stora-Tyutin (BRST) supersymmetry, we prove the general
equivalence of TAP and replica partition functions, and show that the annealed
calculation of the TAP complexity is formally identical to the quenched
thermodynamic calculation of the free energy at one step level of replica
symmetry breaking. The complexity we obtain by means of the BRST symmetry turns
out to be considerably smaller than the previous non-symmetric value. | cond-mat_dis-nn |
Laser Excitation of Polarization Waves in a Frozen Gas: Laser experiments with optically excited frozen gases entail the excitation
of polarization waves. In a continuum approximation the waves are
dispersionless, but their frequency depends on the direction of the propagation
vector. An outline is given of the theory of transient phenomena that involve
the excitation of these waves by a resonant dipole-dipole transfer process. | cond-mat_dis-nn |
Spontaneous and stimulus-induced coherent states of critically balanced
neuronal networks: How the information microscopically processed by individual neurons is
integrated and used in organizing the behavior of an animal is a central
question in neuroscience. The coherence of neuronal dynamics over different
scales has been suggested as a clue to the mechanisms underlying this
integration. Balanced excitation and inhibition may amplify microscopic
fluctuations to a macroscopic level, thus providing a mechanism for generating
coherent multiscale dynamics. Previous theories of brain dynamics, however,
were restricted to cases in which inhibition dominated excitation and
suppressed fluctuations in the macroscopic population activity. In the present
study, we investigate the dynamics of neuronal networks at a critical point
between excitation-dominant and inhibition-dominant states. In these networks,
the microscopic fluctuations are amplified by the strong excitation and
inhibition to drive the macroscopic dynamics, while the macroscopic dynamics
determine the statistics of the microscopic fluctuations. Developing a novel
type of mean-field theory applicable to this class of interscale interactions,
we show that the amplification mechanism generates spontaneous, irregular
macroscopic rhythms similar to those observed in the brain. Through the same
mechanism, microscopic inputs to a small number of neurons effectively entrain
the dynamics of the whole network. These network dynamics undergo a
probabilistic transition to a coherent state, as the magnitude of either the
balanced excitation and inhibition or the external inputs is increased. Our
mean-field theory successfully predicts the behavior of this model.
Furthermore, we numerically demonstrate that the coherent dynamics can be used
for state-dependent read-out of information from the network. These results
show a novel form of neuronal information processing that connects neuronal
dynamics on different scales. | cond-mat_dis-nn |
Experimental Studies of Artificial Spin Ice: Artificial spin ices were originally introduced as analogs of the pyrochlore
spin ices, but have since become a much richer field . The original attraction
of building nanotechnological analogs of the pyrochlores were threefold: to
allow room temperature studies of geometrical frustration; to provide model
statistical mechanical systems where all the relevant parameters in an
experiment can be tuned by design; and to be able to examine the exact
microstate of those systems using advanced magnetic microscopy methods. From
this beginning the field has grown to encompass studies of the effects of
quenched disorder, thermally activated dynamics, microwave frequency responses,
magnetotransport properties, and the development of lattice geometries--with
related emergent physics---that have no analog in naturally-occurring
crystalline systems. The field also offers the prospect of contributing to
novel magnetic logic devices, since the arrays of nanoislands that form
artificial spin ices are similar in many respects to those that are used in the
development of magnetic quantum cellular automata. In this chapter, I review
the experimental aspects of this story, complementing the theoretical chapter
by Gia-Wei Chern. | cond-mat_dis-nn |
Critical scaling in random-field systems: 2 or 3 independent exponents?: We show that the critical scaling behavior of random-field systems with
short-range interactions and disorder correlations cannot be described in
general by only two independent exponents, contrary to previous claims. This
conclusion is based on a theoretical description of the whole (d,N) domain of
the d-dimensional random-field O(N) model and points to the role of rare events
that are overlooked by the proposed derivations of two-exponent scaling. Quite
strikingly, however, the numerical estimates of the critical exponents of the
random field Ising model are extremely close to the predictions of the
two-exponent scaling, so that the issue cannot be decided on the basis of
numerical simulations. | cond-mat_dis-nn |
Mean field theory for the three-dimensional Coulomb glass: We study the low temperature phase of the 3D Coulomb glass within a mean
field approach which reduces the full problem to an effective single site model
with a non-trivial replica structure. We predict a finite glass transition
temperature $T_c$, and a glassy low temperature phase characterized by
permanent criticality. The latter is shown to assure the saturation of the
Efros-Shklovskii Coulomb gap in the density of states. We find this pseudogap
to be universal due to a fixed point in Parisi's flow equations. The latter is
given a physical interpretation in terms of a dynamical self-similarity of the
system in the long time limit, shedding new light on the concept of effective
temperature. From the low temperature solution we infer properties of the
hierarchical energy landscape, which we use to make predictions about the
master function governing the aging in relaxation experiments. | cond-mat_dis-nn |
Direct sampling of complex landscapes at low temperatures: the
three-dimensional +/-J Ising spin glass: A method is presented, which allows to sample directly low-temperature
configurations of glassy systems, like spin glasses. The basic idea is to
generate ground states and low lying excited configurations using a heuristic
algorithm. Then, with the help of microcanonical Monte Carlo simulations, more
configurations are found, clusters of configurations are determined and
entropies evaluated. Finally equilibrium configuration are randomly sampled
with proper Gibbs-Boltzmann weights.
The method is applied to three-dimensional Ising spin glasses with +- J
interactions and temperatures T<=0.5. The low-temperature behavior of this
model is characterized by evaluating different overlap quantities, exhibiting a
complex low-energy landscape for T>0, while the T=0 behavior appears to be less
complex. | cond-mat_dis-nn |
Fluctuation-Induced Interactions and the Spin Glass Transition in
$Fe_2TiO_5$: We investigate the spin-glass transition in the strongly frustrated
well-known compound $Fe_2TiO_5$. A remarkable feature of this transition,
widely discussed in the literature, is its anisotropic properties: the
transition manifests itself in the magnetic susceptibly only along one axis,
despite $Fe^{3+}$ $d^5$ spins having no orbital component. We demonstrate,
using neutron scattering, that below the transition temperature $T_g = 55 K$,
$Fe_2TiO_5$ develops nanoscale surfboard shaped antiferromagnetic regions in
which the $Fe^{3+}$ spins are aligned perpendicular to the axis which exhibits
freezing. We show that the glass transition may result from the freezing of
transverse fluctuations of the magnetization of these regions and we develop a
mean-field replica theory of such a transition, revealing a type of magnetic
van der Waals effect. | cond-mat_dis-nn |
Non-Gaussian effects and multifractality in the Bragg glass: We study, beyond the Gaussian approximation, the decay of the translational
order correlation function for a d-dimensional scalar periodic elastic system
in a disordered environment. We develop a method based on functional
determinants, equivalent to summing an infinite set of diagrams. We obtain, in
dimension d=4-epsilon, the even n-th cumulant of relative displacements as
<[u(r)-u(0)]^n>^c = A_n ln r, with A_n = -(\epsilon/3)^n \Gamma(n-1/2)
\zeta(2n-3)/\pi^(1/2), as well as the multifractal dimension x_q of the
exponential field e^{q u(r)}. As a corollary, we obtain an analytic expression
for a class of n-loop integrals in d=4, which appear in the perturbative
determination of Konishi amplitudes, also accessible via AdS/CFT using
integrability. | cond-mat_dis-nn |
Universal Features of Terahertz Absorption in Disordered Materials: Using an analytical theory, experimental terahertz time-domain spectroscopy
data and numerical evidence, we demonstrate that the frequency dependence of
the absorption coupling coefficient between far-infrared photons and atomic
vibrations in disordered materials has the universal functional form, C(omega)
= A + B*omega^2, where the material-specific constants A and B are related to
the distributions of fluctuating charges obeying global and local charge
neutrality, respectively. | cond-mat_dis-nn |
Magnetic dot arrays modeling via the system of the radial basis function
networks: Two dimensional square lattice general model of the magnetic dot array is
introduced. In this model the intradot self-energy is predicted via the neural
network and interdot magnetostatic coupling is approximated by the collection
of several dipolar terms. The model has been applied to disk-shaped cluster
involving 193 ultrathin dots and 772 interaction centers. In this case among
the intradot magnetic structures retrieved by neural networks the important
role play single-vortex magnetization modes. Several aspects of the model have
been understood numerically by means of the simulated annealing method. | cond-mat_dis-nn |
Statistics of cycles in large networks: We present a Markov Chain Monte Carlo method for sampling cycle length in
large graphs. Cycles are treated as microstates of a system with many degrees
of freedom. Cycle length corresponds to energy such that the length histogram
is obtained as the density of states from Metropolis sampling. In many growing
networks, mean cycle length increases algebraically with system size. The cycle
exponent $\alpha$ is characteristic of the local growth rules and not
determined by the degree exponent $\gamma$. For example, $\alpha=0.76(4)$ for
the Internet at the Autonomous Systems level. | cond-mat_dis-nn |
Bath-induced decay of Stark many-body localization: We investigate the relaxation dynamics of an interacting Stark-localized
system coupled to a dephasing bath, and compare its behavior to the
conventional disorder-induced many body localized system. Specifically, we
study the dynamics of population imbalance between even and odd sites, and the
growth of the von Neumann entropy. For a large potential gradient, the
imbalance is found to decay on a time scale that grows quadratically with the
Wannier-Stark tilt. For the non-interacting system, it shows an exponential
decay, which becomes a stretched exponential decay in the presence of finite
interactions. This is different from a system with disorder-induced
localization, where the imbalance exhibits a stretched exponential decay also
for vanishing interactions. As another clear qualitative difference, we do not
find a logarithmically slow growth of the von-Neumann entropy as it is found
for the disordered system. Our findings can immediately be tested
experimentally with ultracold atoms in optical lattices. | cond-mat_dis-nn |
Continuum Field Model of Street Canyon: Theoretical Description; Part I: A general proecological urban road traffic control idea for the street canyon
is proposed with emphasis placed on development of advanced continuum field
gasdynamical (hydrodynamical) control model of the street canyon. The continuum
field model of optimal control of street canyon is studied. The mathematical
physics' approach (Eulerian approach) to vehicular movement, to pollutants'
emission, and to pollutants' dynamics is used. The rigorous mathematical model
is presented, using gasdynamical (hydrodynamical) theory for both air
constituents and vehicles, including many types of vehicles and many types of
pollutant (exhaust gases) emitted from vehicles. The six optimal control
problems are formulated. | cond-mat_dis-nn |
Critical behaviour and ultrametricity of Ising spin-glass with
long-range interactions: Ising spin-glass systems with long-range interactions ($J(r)\sim
r^{-\sigma}$) are considered. A numerical study of the critical behaviour is
presented in the non-mean-field region together with an analysis of the
probability distribution of the overlaps and of the ultrametric structure of
the space of the equilibrium configurations in the frozen phase. Also in
presence of diverging thermodynamical fluctuations at the critical point the
behaviour of the model is shown to be of the Replica Simmetry Breaking type and
there are hints of a non-trivial ultrametric structure. The parallel tempering
algorithm has been used to simulate the dynamical approach to equilibrium of
such systems. | cond-mat_dis-nn |
Localization and delocalization in one-dimensional systems with
translation-invariant hopping: We present a theory of Anderson localization on a one-dimensional lattice
with translation-invariant hopping. We find by analytical calculation, the
localization length for arbitrary finite-range hopping in the single
propagating channel regime. Then by examining the convergence of the
localization length, in the limit of infinite hopping range, we revisit the
problem of localization criteria in this model and investigate the conditions
under which it can be violated. Our results reveal possibilities of having
delocalized states by tuning the long-range hopping. | cond-mat_dis-nn |
Probing spin glasses with heuristic optimization algorithms: A sketch of the chapter appearing under the same heading in the book ``New
Optimization Algorithms in Physics'' (A.K. Hartmann and H. Rieger, Eds.) is
given. After a general introduction to spin glasses, important aspects of
heuristic algorithms for tackling these systems are covered. Some open problems
that one can hope to resolve in the next few years are then considered. | cond-mat_dis-nn |
Specific Heat of Quantum Elastic Systems Pinned by Disorder: We present the detailed study of the thermodynamics of vibrational modes in
disordered elastic systems such as the Bragg glass phase of lattices pinned by
quenched impurities. Our study and our results are valid within the (mean
field) replica Gaussian variational method. We obtain an expression for the
internal energy in the quantum regime as a function of the saddle point
solution, which is then expanded in powers of $\hbar$ at low temperature $T$.
In the calculation of the specific heat $C_v$ a non trivial cancellation of the
term linear in $T$ occurs, explicitly checked to second order in $\hbar$. The
final result is $C_v \propto T^3$ at low temperatures in dimension three and
two. The prefactor is controlled by the pinning length. This result is
discussed in connection with other analytical or numerical studies. | cond-mat_dis-nn |
Heterogeneous dynamics of the three dimensional Coulomb glass out of
equilibrium: The non-equilibrium relaxational properties of a three dimensional Coulomb
glass model are investigated by kinetic Monte Carlo simulations. Our results
suggest a transition from stationary to non-stationary dynamics at the
equilibrium glass transition temperature of the system. Below the transition
the dynamic correlation functions loose time translation invariance and
electron diffusion is anomalous. Two groups of carriers can be identified at
each time scale, electrons whose motion is diffusive within a selected time
window and electrons that during the same time interval remain confined in
small regions in space. During the relaxation that follows a temperature quench
an exchange of electrons between these two groups takes place and the
non-equilibrium excess of diffusive electrons initially present decreases
logarithmically with time as the system relaxes. This bimodal dynamical
heterogeneity persists at higher temperatures when time translation invariance
is restored and electron diffusion is normal. The occupancy of the two
dynamical modes is then stationary and its temperature dependence reflects a
crossover between a low-temperature regime with a high concentration of
electrons forming fluctuating dipoles and a high-temperature regime in which
the concentration of diffusive electrons is high. | cond-mat_dis-nn |
Random transverse-field Ising chain with long-range interactions: We study the low-energy properties of the long-range random transverse-field
Ising chain with ferromagnetic interactions decaying as a power alpha of the
distance. Using variants of the strong-disorder renormalization group method,
the critical behavior is found to be controlled by a strong-disorder fixed
point with a finite dynamical exponent z_c=alpha. Approaching the critical
point, the correlation length diverges exponentially. In the critical point,
the magnetization shows an alpha-independent logarithmic finite-size scaling
and the entanglement entropy satisfies the area law. These observations are
argued to hold for other systems with long-range interactions, even in higher
dimensions. | cond-mat_dis-nn |
Localization properties of the asymptotic density distribution of a
one-dimensional disordered system: Anderson localization is the ubiquitous phenomenon of inhibition of transport
of classical and quantum waves in a disordered medium. In dimension one, it is
well known that all states are localized, implying that the distribution of an
initially narrow wave-packet released in a disordered potential will, at long
time, decay exponentially on the scale of the localization length. However, the
exact shape of the stationary localized distribution differs from a purely
exponential profile and has been computed almost fifty years ago by Gogolin.
Using the atomic quantum kicked rotor, a paradigmatic quantum simulator of
Anderson localization physics, we study this asymptotic distribution by two
complementary approaches. First, we discuss the connection of the statistical
properties of the system's localized eigenfunctions and their exponential decay
with the localization length of the Gogolin distribution. Next, we make use of
our experimental platform, realizing an ideal Floquet disordered system, to
measure the long-time probability distribution and highlight the very good
agreement with the analytical prediction compared to the purely exponential one
over 3 orders of magnitude. | cond-mat_dis-nn |
Correlation length of the two-dimensional Ising spin glass with bimodal
interactions: We study the correlation length of the two-dimensional Edwards-Anderson Ising
spin glass with bimodal interactions using a combination of parallel tempering
Monte Carlo and a rejection-free cluster algorithm in order to speed up
equilibration. Our results show that the correlation length grows ~ exp(2J/T)
suggesting through hyperscaling that the degenerate ground state is separated
from the first excited state by an energy gap ~4J, as would naively be
expected. | cond-mat_dis-nn |
Memories of initial states and density imbalance in dynamics of
interacting disordered systems: We study the dynamics of one and two dimensional disordered lattice
bosons/fermions initialized to a Fock state with a pattern of $1$ and $0$
particles on $A$ and ${\bar A}$ sites. For non-interacting systems we establish
a universal relation between the long time density imbalance between $A$ and
${\bar A}$ site, $I(\infty)$, the localization length $\xi_l$, and the geometry
of the initial pattern. For alternating initial pattern of $1$ and $0$
particles in 1 dimension, $I(\infty)=\tanh[a/\xi_l]$, where $a$ is the lattice
spacing. For systems with mobility edge, we find analytic relations between
$I(\infty)$, the effective localization length $\tilde{\xi}_l$ and the fraction
of localized states $f_l$. The imbalance as a function of disorder shows
non-analytic behaviour when the mobility edge passes through a band edge. For
interacting bosonic systems, we show that dissipative processes lead to a decay
of the memory of initial conditions. However, the excitations created in the
process act as a bath, whose noise correlators retain information of the
initial pattern. This sustains a finite imbalance at long times in strongly
disordered interacting systems. | cond-mat_dis-nn |
Resonant metallic states in driven quasiperiodic lattices: We consider a quasiperiodic Aubry-Andre (AA) model and add a weak
time-periodic and spatially quasiperiodic perturbation. The undriven AA model
is chosen to be well in the insulating regime. The spatial quasiperiodic
perturbation extends the model into two dimensions in reciprocal space. For a
spatial resonance which reduces the reciprocal space dynamics to an effective
one-dimensional two-leg ladder case, the ac perturbation resonantly couples
certain groups of localized eigenstates of the undriven AA model and turns them
into extended metallic ones. Slight detuning of the spatial and temporal
frequencies off resonance returns these states into localized ones. We analyze
the details of the resonant metallic eigenstates using Floquet representations.
In particular, we find that their size grows linearly with the system size.
Initial wave packets overlap with resonant metallic eigenstates and lead to
ballistic spreading. | cond-mat_dis-nn |
Method to solve quantum few-body problems with artificial neural
networks: A machine learning technique to obtain the ground states of quantum few-body
systems using artificial neural networks is developed. Bosons in continuous
space are considered and a neural network is optimized in such a way that when
particle positions are input into the network, the ground-state wave function
is output from the network. The method is applied to the Calogero-Sutherland
model in one-dimensional space and Efimov bound states in three-dimensional
space. | cond-mat_dis-nn |
Evidence for existence of many pure ground states in 3d $\pm J$ Spin
Glasses: Ground states of 3d EA Ising spin glasses are calculated for sizes up to
$14^3$ using a combination of genetic algorithms and cluster-exact
approximation . The distribution $P(|q|)$ of overlaps is calculated. For
increasing size the width of $P(|q|)$ converges to a nonzero value, indicating
that many pure ground states exist for short range Ising spin glasses. | cond-mat_dis-nn |
The number of guards needed by a museum: A phase transition in vertex
covering of random graphs: In this letter we study the NP-complete vertex cover problem on finite
connectivity random graphs. When the allowed size of the cover set is
decreased, a discontinuous transition in solvability and typical-case
complexity occurs. This transition is characterized by means of exact numerical
simulations as well as by analytical replica calculations. The replica
symmetric phase diagram is in excellent agreement with numerical findings up to
average connectivity $e$, where replica symmetry becomes locally unstable. | cond-mat_dis-nn |
Testing a Variational Approach to Random Directed Polymers: The one dimensional direct polymer in random media model is investigated
using a variational approach in the replica space. We demonstrate numerically
that the stable point is a maximum and the corresponding statistical properties
for the delta correlated potential are in good agreements with the known
analytic solution. In the case of power-law correlated potential two regimes
are recovered: a Flory scaling dependent on the exponent of the correlations,
and a short range regime in analogy with the delta-correlated potential case. | cond-mat_dis-nn |
Comment on "Disorder Induced Quantum Phase Transition in Random-Exchange
Spin-1/2 Chains": We reconsider the random bond antiferromagnetic spin-1/2 chain for weak
disorder and demonstrate the existence of crossover length scale x_W that
diverges with decreasing strength of the disorder. Recent DMRG calculations
[Phys. Rev. Lett. 89, 127202 (2002); cond-mat/0111027] claimed to have found
evidence for a non-universal behavior in this model and found no indications of
a universal infinite randomness fixed point (IRFP) scenario. We show that these
data are not in the asymptotic regime since the system sizes that have been
considered are of the same order of magnitude or much smaller than the
crossover length x_W. We give a scaling form for the xx-spin-correlation
function that takes this crossover length into account and that is compatible
with the IRFP scenario and a random singlet phase. | cond-mat_dis-nn |
Atomic level structure of Ge-Sb-S glasses: chemical short range order
and long Sb-S bonds: The structure of Ge$_{20}$Sb$_{10}$S$_{70}$, Ge$_{23}$Sb$_{12}$S$_{65}$ and
Ge$_{26}$Sb$_{13}$S$_{61}$ glasses was investigated by neutron diffraction
(ND), X-ray diffraction (XRD), extended X-ray absorption fine structure (EXAFS)
measurements at the Ge and Sb K-edges as well as Raman scattering. For each
composition, large scale structural models were obtained by fitting
simultaneously diffraction and EXAFS data sets in the framework of the reverse
Monte Carlo (RMC) simulation technique. Ge and S atoms have 4 and 2 nearest
neighbors, respectively. The structure of these glasses can be described by the
chemically ordered network model: Ge-S and Sb-S bonds are always preferred.
These two bond types adequately describe the structure of the stoichiometric
glass while S-S bonds can also be found in the S-rich composition. Raman
scattering data show the presence of Ge-Ge, Ge-Sb and Sb-Sb bonds in the
S-deficient glass but only Ge-Sb bonds are needed to fit diffraction and EXAFS
datasets. A significant part of the Sb-S pairs has 0.3-0.4 {\AA} longer bond
distance than the usually accepted covalent bond length (~2.45 {\AA}). From
this observation it was inferred that a part of Sb atoms have more than 3 S
neighbors. | cond-mat_dis-nn |
Polaritons in 2D-crystals and localized modes in narrow waveguides: We study 2D-polaritons in an atomically thin dipole-active layer (2D-crystal)
placed inside a parallel-plate wavegude, and investigate the possibility to
obtain the localized wavegude modes associated with atomic defects. Considering
the wavegude width, $l,$ as an adjustable parameter, we show that in the
waveguide with $l\sim 10^{4} a,$ where $a$ is the lattice parameter, the
localized mode can be provided by a single impurity or a local structural
defect. | cond-mat_dis-nn |
Mean Field Theory of the Three-Dimensional Dipole Superspin Glasses: We study the three-dimensional system of magnetic nanoparticle dipoles
randomly oriented along quenched easy axes. Directions of the magnetic momenta
are described by the Ising variables which allow the momenta to flip along
their random orientations. Using the standard mean-field approximation and the
replica technique it is shown that the system undergoes a finite temperature
phase transition into a spin-glass phase. | cond-mat_dis-nn |
Tunneling and Non-Universality in Continuum Percolation Systems: The values obtained experimentally for the conductivity critical exponent in
numerous percolation systems, in which the interparticle conduction is by
tunnelling, were found to be in the range of $t_0$ and about $t_0+10$, where
$t_0$ is the universal conductivity exponent. These latter values are however
considerably smaller than those predicted by the available ``one
dimensional"-like theory of tunneling-percolation. In this letter we show that
this long-standing discrepancy can be resolved by considering the more
realistic "three dimensional" model and the limited proximity to the
percolation threshold in all the many available experimental studies | cond-mat_dis-nn |
Origin of the computational hardness for learning with binary synapses: Supervised learning in a binary perceptron is able to classify an extensive
number of random patterns by a proper assignment of binary synaptic weights.
However, to find such assignments in practice, is quite a nontrivial task. The
relation between the weight space structure and the algorithmic hardness has
not yet been fully understood. To this end, we analytically derive the
Franz-Parisi potential for the binary preceptron problem, by starting from an
equilibrium solution of weights and exploring the weight space structure around
it. Our result reveals the geometrical organization of the weight
space\textemdash the weight space is composed of isolated solutions, rather
than clusters of exponentially many close-by solutions. The point-like clusters
far apart from each other in the weight space explain the previously observed
glassy behavior of stochastic local search heuristics. | cond-mat_dis-nn |
Scaling hypothesis for the Euclidean bipartite matching problem II.
Correlation functions: We analyze the random Euclidean bipartite matching problem on the hypertorus
in $d$ dimensions with quadratic cost and we derive the two--point correlation
function for the optimal matching, using a proper ansatz introduced by
Caracciolo et al. to evaluate the average optimal matching cost. We consider
both the grid--Poisson matching problem and the Poisson--Poisson matching
problem. We also show that the correlation function is strictly related to the
Green's function of the Laplace operator on the hypertorus. | cond-mat_dis-nn |
Hidden dimers and the matrix maps: Fibonacci chains re-visited: The existence of cycles of the matrix maps in Fibonacci class of lattices is
well established. We show that such cycles are intimately connected with the
presence of interesting positional correlations among the constituent `atoms'
in a one dimensional quasiperiodic lattice. We particularly address the
transfer model of the classic golden mean Fibonacci chain where a six cycle of
the full matrix map exists at the centre of the spectrum [Kohmoto et al, Phys.
Rev. B 35, 1020 (1987)], and for which no simple physical picture has so far
been provided, to the best of our knowledge. In addition, we show that our
prescription leads to a determination of other energy values for a mixed model
of the Fibonacci chain, for which the full matrix map may have similar cyclic
behaviour. Apart from the standard transfer-model of a golden mean Fibonacci
chain, we address a variant of it and the silver mean lattice, where the
existence of four cycles of the matrix map is already known to exist. The
underlying positional correlations for all such cases are discussed in details. | cond-mat_dis-nn |
Numerical Solution-Space Analysis of Satisfiability Problems: The solution-space structure of the 3-Satisfiability Problem (3-SAT) is
studied as a function of the control parameter alpha (ratio of number of
clauses to the number of variables) using numerical simulations. For this
purpose, one has to sample the solution space with uniform weight. It is shown
here that standard stochastic local-search (SLS) algorithms like "ASAT" and
"MCMCMC" (also known as "parallel tempering") exhibit a sampling bias.
Nevertheless, unbiased samples of solutions can be obtained using the
"ballistic-networking approach", which is introduced here. It is a
generalization of "ballistic search" methods and yields also a cluster
structure of the solution space. As application, solutions of 3-SAT instances
are generated using ASAT plus ballistic networking. The numerical results are
compatible with a previous analytic prediction of a simple solution-space
structure for small values of alpha and a transition to a clustered phase at
alpha_c ~ 3.86, where the solution space breaks up into several non-negligible
clusters. Furthermore, in the thermodynamic limit there are, for values of
alpha close to the SATUNSAT transition alpha_s ~ 4.267, always clusters without
any frozen variables. This may explain why some SLS algorithms are able to
solve very large 3-SAT instances close to the SAT-UNSAT transition. | cond-mat_dis-nn |
Spatio-temporal correlations in Wigner molecules: The dynamical response of Coulomb-interacting particles in nano-clusters are
analyzed at different temperatures characterizing their solid- and liquid-like
behavior. Depending on the trap-symmetry, both the spatial and temporal
correlations undergo slow, stretched exponential relaxations at long times,
arising from spatially correlated motion in string-like paths. Our results
indicate that the distinction between the `solid' and `liquid' is soft: While
particles in a `solid' flow producing dynamic heterogeneities, motion in
`liquid' yields unusually long tail in the distribution of
particle-displacements. A phenomenological model captures much of the
subtleties of our numerical simulations. | cond-mat_dis-nn |
Anisotropic Magnetoconductance in Quench-Condensed Ultrathin Beryllium
Films: Near the superconductor-insulator (S-I) transition, quench-condensed
ultrathin Be films show a large magnetoconductance which is highly anisotropic
in the direction of the applied field. Film conductance can drop as much as
seven orders of magnitude in a weak perpendicular field (< 1 T), but is
insensitive to a parallel field in the same field range. We believe that this
negative magnetoconductance is due to the field de-phasing of the
superconducting pair wavefunction. This idea enables us to extract the finite
superconducting phase coherence length in nearly superconducting films. Our
data indicate that this local phase coherence persists even in highly
insulating films in the vicinity of the S-I transition. | cond-mat_dis-nn |
Short-range Magnetic interactions in the Spin-Ice compound
Ho$_{2}$Ti$_{2}$O$_{7}$: Magnetization and susceptibility studies on single crystals of the pyrochlore
Ho$_{2}$Ti$_{2}$O$_{7}$ are reported for the first time. Magnetization
isotherms are shown to be qualitatively similar to that predicted by the
nearest neighbor spin-ice model. Below the lock-in temperature, $T^{\ast
}\simeq 1.97$ K, magnetization is consistent with the locking of spins along
[111] directions in a specific two-spins-in, two-spins-out arrangement. Below
$T^{\ast}$ the magnetization for $B||[111]$ displays a two step behavior
signalling the breaking of the ice rules. | cond-mat_dis-nn |
Chaos in Glassy Systems from a TAP Perspective: We discuss level crossing of the free-energy of TAP solutions under
variations of external parameters such as magnetic field or temperature in
mean-field spin-glass models that exhibit one-step Replica-Symmetry-Breaking
(1RSB). We study the problem through a generalized complexity that describes
the density of TAP solutions at a given value of the free-energy and a given
value of the extensive quantity conjugate to the external parameter. We show
that variations of the external parameter by any finite amount can induce level
crossing between groups of TAP states whose free-energies are extensively
different. In models with 1RSB, this means strong chaos with respect to the
perturbation. The linear-response induced by extensive level crossing is
self-averaging and its value matches precisely with the disorder-average of the
non self-averaging anomaly computed from the 2nd moment of thermal fluctuations
between low-lying, almost degenerate TAP states. We present an analytical
recipe to compute the generalized complexity and test the scenario on the
spherical multi-$p$ spin models under variation of temperature. | cond-mat_dis-nn |
Modified spin-wave study of random antiferromagnetic-ferromagnetic spin
chains: We study the thermodynamics of one-dimensional quantum spin-1/2 Heisenberg
ferromagnetic system with random antiferromagnetic impurity bonds. In the
dilute impurity limit, we generalize the modified spin-wave theory for random
spin chains, where local chemical potentials for spin-waves in ferromagnetic
spin segments are introduced to ensure zero magnetization at finite
temperature. This approach successfully describes the crossover from behavior
of pure one-dimensional ferromagnet at high temperatures to a distinct Curie
behavior due to randomness at low temperatures. We discuss the effects of
impurity bond strength and concentration on the crossover and low temperature
behavior. | cond-mat_dis-nn |
Spin-Glass Phase in the Random Temperature Ising Ferromagnet: In this paper we study the phase diagram of the disordered Ising ferromagnet.
Within the framework of the Gaussian variational approximation it is shown that
in systems with a finite value of the disorder in dimensions D=4 and D < 4 the
paramagnetic and ferromagnetic phases are separated by a spin-glass phase. The
transition from paramagnetic to spin-glass state is continuous (second-order),
while the transition between spin-glass and ferromagnetic states is
discontinuous (first-order). It is also shown that within the considered
approximation there is no replica symmetry breaking in the spin-glass phase.
The validity of the Gaussian variational approximation for the present problem
is discussed, and we provide a tentative physical interpretation of the
results. | cond-mat_dis-nn |
Phase transitions induced by microscopic disorder: a study based on the
order parameter expansion: Based on the order parameter expansion, we present an approximate method
which allows us to reduce large systems of coupled differential equations with
diverse parameters to three equations: one for the global, mean field, variable
and two which describe the fluctuations around this mean value. With this tool
we analyze phase-transitions induced by microscopic disorder in three
prototypical models of phase-transitions which have been studied previously in
the presence of thermal noise. We study how macroscopic order is induced or
destroyed by time independent local disorder and analyze the limits of the
approximation by comparing the results with the numerical solutions of the
self-consistency equation which arises from the property of self-averaging.
Finally, we carry on a finite-size analysis of the numerical results and
calculate the corresponding critical exponents. | cond-mat_dis-nn |
Are Mean-Field Spin-Glass Models Relevant for the Structural Glass
Transition?: We analyze the properties of the energy landscape of {\it finite-size} fully
connected p-spin-like models whose high temperature phase is described, in the
thermodynamic limit, by the schematic Mode Coupling Theory of super-cooled
liquids. We show that {\it finite-size} fully connected p-spin-like models,
where activated processes are possible, do exhibit properties typical of real
super-cooled liquid when both are near the critical glass transition. Our
results support the conclusion that fully-connected p-spin-like models are the
natural statistical mechanical models for studying the glass transition in
super-cooled liquids. | cond-mat_dis-nn |
Curie Temperature for Small World Ising Systems of Different Dimensions: For Small World Ising systems of different dimensions, "concentration"
dependencies T_C(p) of the Curie temperature upon the fraction p of long-range
links have been derived on a basis of simple physical considerations. We have
found T_C(p) ~ 1/ln|p| for 1D, T_C(p) ~ p^{1/2} for 2D, and T_C(p) ~ p^{2/3}
for 3D. | cond-mat_dis-nn |
The Centred Traveling Salesman at Finite Temperature: A recently formulated statistical mechanics method is used to study the phase
transition occurring in a generalisation of the Traveling Salesman Problem
(TSP) known as the centred TSP. The method shows that the problem has clear
signs of a crossover, but is only able to access (unscaled) finite temperatures
above the transition point. The solution of the problem using this method
displays a curious duality. | cond-mat_dis-nn |
Fluctuations analysis in complex networks modeled by hidden variable
models. Necessity of a large cut-off in hidden-variable models: It is becoming more and more clear that complex networks present remarkable
large fluctuations. These fluctuations may manifest differently according to
the given model. In this paper we re-consider hidden variable models which turn
out to be more analytically treatable and for which we have recently shown
clear evidence of non-self averaging; the density of a motif being subject to
possible uncontrollable fluctuations in the infinite size limit. Here we
provide full detailed calculations and we show that large fluctuations are only
due to the node hidden variables variability while, in ensembles where these
are frozen, fluctuations are negligible in the thermodynamic limit, and equal
the fluctuations of classical random graphs. A special attention is paid to the
choice of the cut-off: we show that in hidden-variable models, only a cut-off
growing as $N^\lambda$ with $\lambda\geq 1$ can reproduce the scaling of a
power-law degree distribution. In turn, it is this large cut-off that generates
non-self-averaging. | cond-mat_dis-nn |
Critical dynamics of the k-core pruning process: We present the theory of the k-core pruning process (progressive removal of
nodes with degree less than k) in uncorrelated random networks. We derive exact
equations describing this process and the evolution of the network structure,
and solve them numerically and, in the critical regime of the process,
analytically. We show that the pruning process exhibits three different
behaviors depending on whether the mean degree <q> of the initial network is
above, equal to, or below the threshold <q>_c corresponding to the emergence of
the giant k-core. We find that above the threshold the network relaxes
exponentially to the k-core. The system manifests the phenomenon known as
"critical slowing down", as the relaxation time diverges when <q> tends to
<q>_c. At the threshold, the dynamics become critical characterized by a
power-law relaxation (1/t^2). Below the threshold, a long-lasting transient
process (a "plateau" stage) occurs. This transient process ends with a collapse
in which the entire network disappears completely. The duration of the process
diverges when <q> tends to <q>_c. We show that the critical dynamics of the
pruning are determined by branching processes of spreading damage. Clusters of
nodes of degree exactly k are the evolving substrate for these branching
processes. Our theory completely describes this branching cascade of damage in
uncorrelated networks by providing the time dependent distribution function of
branching. These theoretical results are supported by our simulations of the
$k$-core pruning in Erdos-Renyi graphs. | cond-mat_dis-nn |
Effects of substrate network topologies on competition dynamics: We study a competition dynamics, based on the minority game, endowed with
various substrate network structures. We observe the effects of the network
topologies by investigating the volatility of the system and the structure of
follower networks. The topology of substrate structures significantly
influences the system efficiency represented by the volatility and such
substrate networks are shown to amplify the herding effect and cause
inefficiency in most cases. The follower networks emerging from the leadership
structure show a power-law incoming degree distribution. This study shows the
emergence of scale-free structures of leadership in the minority game and the
effects of the interaction among players on the networked version of the game. | cond-mat_dis-nn |
The Physics of Living Neural Networks: Improvements in technique in conjunction with an evolution of the theoretical
and conceptual approach to neuronal networks provide a new perspective on
living neurons in culture. Organization and connectivity are being measured
quantitatively along with other physical quantities such as information, and
are being related to function. In this review we first discuss some of these
advances, which enable elucidation of structural aspects. We then discuss two
recent experimental models that yield some conceptual simplicity. A
one-dimensional network enables precise quantitative comparison to analytic
models, for example of propagation and information transport. A two-dimensional
percolating network gives quantitative information on connectivity of cultured
neurons. The physical quantities that emerge as essential characteristics of
the network in vitro are propagation speeds, synaptic transmission, information
creation and capacity. Potential application to neuronal devices is discussed. | cond-mat_dis-nn |
Statistical Mechanics of the Bayesian Image Restoration under Spatially
Correlated Noise: We investigated the use of the Bayesian inference to restore noise-degraded
images under conditions of spatially correlated noise. The generative
statistical models used for the original image and the noise were assumed to
obey multi-dimensional Gaussian distributions whose covariance matrices are
translational invariant. We derived an exact description to be used as the
expectation for the restored image by the Fourier transformation and restored
an image distorted by spatially correlated noise by using a spatially
uncorrelated noise model. We found that the resulting hyperparameter
estimations for the minimum error and maximal posterior marginal criteria did
not coincide when the generative probabilistic model and the model used for
restoration were in different classes, while they did coincide when they were
in the same class. | cond-mat_dis-nn |
Interpolating between boolean and extremely high noisy patterns through
Minimal Dense Associative Memories: Recently, Hopfield and Krotov introduced the concept of {\em dense
associative memories} [DAM] (close to spin-glasses with $P$-wise interactions
in a disordered statistical mechanical jargon): they proved a number of
remarkable features these networks share and suggested their use to (partially)
explain the success of the new generation of Artificial Intelligence. Thanks to
a remarkable ante-litteram analysis by Baldi \& Venkatesh, among these
properties, it is known these networks can handle a maximal amount of stored
patterns $K$ scaling as $K \sim N^{P-1}$.\\ In this paper, once introduced a
{\em minimal dense associative network} as one of the most elementary
cost-functions falling in this class of DAM, we sacrifice this high-load regime
-namely we force the storage of {\em solely} a linear amount of patterns, i.e.
$K = \alpha N$ (with $\alpha>0$)- to prove that, in this regime, these networks
can correctly perform pattern recognition even if pattern signal is $O(1)$ and
is embedded in a sea of noise $O(\sqrt{N})$, also in the large $N$ limit. To
prove this statement, by extremizing the quenched free-energy of the model over
its natural order-parameters (the various magnetizations and overlaps), we
derived its phase diagram, at the replica symmetric level of description and in
the thermodynamic limit: as a sideline, we stress that, to achieve this task,
aiming at cross-fertilization among disciplines, we pave two hegemon routes in
the statistical mechanics of spin glasses, namely the replica trick and the
interpolation technique.\\ Both the approaches reach the same conclusion: there
is a not-empty region, in the noise-$T$ vs load-$\alpha$ phase diagram plane,
where these networks can actually work in this challenging regime; in
particular we obtained a quite high critical (linear) load in the (fast)
noiseless case resulting in $\lim_{\beta \to \infty}\alpha_c(\beta)=0.65$. | cond-mat_dis-nn |
Analytic Solution to Clustering Coefficients on Weighted Networks: Clustering coefficient is an important topological feature of complex
networks. It is, however, an open question to give out its analytic expression
on weighted networks yet. Here we applied an extended mean-field approach to
investigate clustering coefficients in the typical weighted networks proposed
by Barrat, Barth\'elemy and Vespignani (BBV networks). We provide analytical
solutions of this model and find that the local clustering in BBV networks
depends on the node degree and strength. Our analysis is well in agreement with
results of numerical simulations. | cond-mat_dis-nn |
Direct topological insulator transitions in three dimensions are
destabilized by non-perturbative effects of disorder: We reconsider the phase diagram of a three-dimensional $\mathbb{Z}_2$
topological insulator in the presence of short-ranged potential disorder with
the insight that non-perturbative rare states destabilize the noninteracting
Dirac semimetal critical point separating different topological phases. Based
on our numerical data on the density of states, conductivity, and
wavefunctions, we argue that the putative Dirac semimetal line is destabilized
into a diffusive metal phase of finite extent due to non-perturbative effects
of rare regions. We discuss the implications of these results for past and
current experiments on doped topological insulators. | 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 |
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 |
Properties of equilibria and glassy phases of the random Lotka-Volterra
model with demographic noise: In this letter we study a reference model in theoretical ecology, the
disordered Lotka-Volterra model for ecological communities, in the presence of
finite demographic noise. Our theoretical analysis, which takes advantage of a
mapping to an equilibrium disordered system, proves that for sufficiently
heterogeneous interactions and low demographic noise the system displays a
multiple equilibria phase, which we fully characterize. In particular, we show
that in this phase the number of stable equilibria is exponential in the number
of species. Upon further decreasing the demographic noise, we unveil a
"Gardner" transition to a marginally stable phase, similar to that observed in
jamming of amorphous materials. We confirm and complement our analytical
results by numerical simulations. Furthermore, we extend their relevance by
showing that they hold for others interacting random dynamical systems, such as
the Random Replicant Model. Finally, we discuss their extension to the case of
asymmetric couplings. | cond-mat_dis-nn |
Weakly driven anomalous diffusion in non-ergodic regime: an analytical
solution: We derive the probability density of a diffusion process generated by
nonergodic velocity fluctuations in presence of a weak potential, using the
Liouville equation approach. The velocity of the diffusing particle undergoes
dichotomic fluctuations with a given distribution $\psi(\tau)$ of residence
times in each velocity state. We obtain analytical solutions for the diffusion
process in a generic external potential and for a generic statistics of
residence times, including the non-ergodic regime in which the mean residence
time diverges. We show that these analytical solutions are in agreement with
numerical simulations. | cond-mat_dis-nn |
Study of off-diagonal disorder using the typical medium dynamical
cluster approximation: We generalize the typical medium dynamical cluster approximation (TMDCA) and
the local Blackman, Esterling, and Berk (BEB) method for systems with
off-diagonal disorder. Using our extended formalism we perform a systematic
study of the effects of non-local disorder-induced correlations and of
off-diagonal disorder on the density of states and the mobility edge of the
Anderson localized states. We apply our method to the three-dimensional
Anderson model with configuration dependent hopping and find fast convergence
with modest cluster sizes. Our results are in good agreement with the data
obtained using exact diagonalization, and the transfer matrix and kernel
polynomial methods. | cond-mat_dis-nn |
Coherent Umklapp Scattering of Light from Disordered Photonic Crystals: A theoretical study of the coherent light scattering from disordered photonic
crystal is presented. In addition to the conventional enhancement of the
reflected light intensity into the backscattering direction, the so called
coherent backscattering (CBS), the periodic modulation of the dielectric
function in photonic crystals gives rise to a qualitatively new effect:
enhancement of the reflected light intensity in directions different from the
backscattering direction. These additional coherent scattering processes,
dubbed here {\em umklapp scattering} (CUS), result in peaks, which are most
pronounced when the incident light beam enters the sample at an angle close to
the the Bragg angle. Assuming that the dielectric function modulation is weak,
we study the shape of the CUS peaks for different relative lengths of the
modulation-induced Bragg attenuation compared to disorder-induced mean free
path. We show that when the Bragg length increases, then the CBS peak assumes
its conventional shape, whereas the CUS peak rapidly diminishes in amplitude.
We also study the suppression of the CUS peak upon the departure of the
incident beam from Bragg resonance: we found that the diminishing of the CUS
intensity is accompanied by substantial broadening. In addition, the peak
becomes asymmetric. | cond-mat_dis-nn |
Multi-overlap simulations of spin glasses: We present results of recent high-statistics Monte Carlo simulations of the
Edwards-Anderson Ising spin-glass model in three and four dimensions. The study
is based on a non-Boltzmann sampling technique, the multi-overlap algorithm
which is specifically tailored for sampling rare-event states. We thus
concentrate on those properties which are difficult to obtain with standard
canonical Boltzmann sampling such as the free-energy barriers F^q_B in the
probability density P_J(q) of the Parisi overlap parameter q and the behaviour
of the tails of the disorder averaged density P(q) = [P_J(q)]_av. | cond-mat_dis-nn |
Eigenvalue Distribution In The Self-Dual Non-Hermitian Ensemble: We consider an ensemble of self-dual matrices with arbitrary complex entries.
This ensemble is closely related to a previously defined ensemble of
anti-symmetric matrices with arbitrary complex entries. We study the two-level
correlation functions numerically. Although no evidence of non-monotonicity is
found in the real space correlation function, a definite shoulder is found. On
the analytical side, we discuss the relationship between this ensemble and the
$\beta=4$ two-dimensional one-component plasma, and also argue that this
ensemble, combined with other ensembles, exhausts the possible universality
classes in non-hermitian random matrix theory. This argument is based on
combining the method of hermitization of Feinberg and Zee with Zirnbauer's
classification of ensembles in terms of symmetric spaces. | cond-mat_dis-nn |
Temperature-Dependent Defect Dynamics in the Network Glass SiO2: We investigate the long time dynamics of a strong glass former, SiO2, below
the glass transition temperature by averaging single particle trajectories over
time windows which comprise roughly 100 particle oscillations. The structure on
this coarse-grained time scale is very well defined in terms of coordination
numbers, allowing us to identify ill-coordinated atoms, called defects in the
following. The most numerous defects are OO neighbors, whose lifetimes are
comparable to the equilibration time at low temperature. On the other hand SiO
and OSi defects are very rare and short lived. The lifetime of defects is found
to be strongly temperature dependent, consistent with activated processes.
Single-particle jumps give rise to local structural rearrangements. We show
that in SiO2 these structural rearrangements are coupled to the creation or
annihilation of defects, giving rise to very strong correlations of jumping
atoms and defects. | cond-mat_dis-nn |
Frustration and sound attenuation in structural glasses: Three classes of harmonic disorder systems (Lennard-Jones like glasses,
percolators above threshold, and spring disordered lattices) have been
numerically investigated in order to clarify the effect of different types of
disorder on the mechanism of high frequency sound attenuation. We introduce the
concept of frustration in structural glasses as a measure of the internal
stress, and find a strong correlation between the degree of frustration and the
exponent alpha that characterizes the momentum dependence of the sound
attenuation $Gamma(Q)$$\simeq$$Q^\alpha$. In particular, alpha decreases from
about d+1 in low-frustration systems (where d is the spectral dimension), to
about 2 for high frustration systems like the realistic glasses examined. | cond-mat_dis-nn |
Rotation Diffusion as an Additional Mechanism of Energy Dissipation in
Polymer Melts: The research is important for a molecular theory of liquid and has a wide
interest as an example solving the problem when dynamic parameters of systems
can be indirectly connected with their equilibrium properties. In frameworks of
the reptation model the power law with the 3.4-exponent for the melt viscosity
relation to the molecular weight of linear flexible-chain polymer is predicted
as distinct from the value 3 expected for a melt of ring macromolecules. To
find the exponent close to experimental values it should be taken into account
the rotation vibration precession motion of chain ends about the polymer melt
flow direction. | cond-mat_dis-nn |
Disorder-Induced Vibrational Localization: The vibrational equivalent of the Anderson tight-binding Hamiltonian has been
studied, with particular focus on the properties of the eigenstates at the
transition from extended to localized states. The critical energy has been
found approximately for several degrees of force-constant disorder using
system-size scaling of the multifractal spectra of the eigenmodes, and the
spectrum at which there is no system-size dependence has been obtained. This is
shown to be in good agreement with the critical spectrum for the electronic
problem, which has been derived both numerically and by analytic means.
Universality of the critical states is therefore suggested also to hold for the
vibrational problem. | cond-mat_dis-nn |
Signs of low frequency dispersions in disordered binary dielectric
mixtures (50-50): Dielectric relaxation in disordered dielectric mixtures are presented by
emphasizing the interfacial polarization. The obtained results coincide with
and cause confusion with those of the low frequency dispersion behavior. The
considered systems are composed of two phases on two-dimensional square and
triangular topological networks. We use the finite element method to calculate
the effective dielectric permittivities of randomly generated structures. The
dielectric relaxation phenomena together with the dielectric permittivity
values at constant frequencies are investigated, and significant differences of
the square and triangular topologies are observed. The frequency dependent
properties of some of the generated structures are examined. We conclude that
the topological disorder may lead to the normal or anomalous low frequency
dispersion if the electrical properties of the phases are chosen properly, such
that for ``slightly'' {\em reciprocal mixture}--when $\sigma_1\gg\sigma_2$, and
$\epsilon_1<\epsilon_2$--normal, and while for ``extreme'' {\em reciprocal
mixture}--when $\sigma_1\gg\sigma_2$, and $\epsilon_1\ll\epsilon_2$--anomalous
low frequency dispersions are obtained. Finally, comparison with experimental
data indicates that one can obtain valuable information from simulations when
the material properties of the constituents are not available and of
importance. | cond-mat_dis-nn |
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