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Momentum distribution of a freely expanding Lieb-Liniger gas: We numerically study free expansion of a few Lieb-Liniger bosons, which are initially in the ground state of an infinitely deep hard-wall trap. Numerical calculation is carried out by employing a standard Fourier transform, as follows from the Fermi-Bose transformation for a time-dependent Lieb-Liniger gas. We study the evolution of the momentum distribution, the real-space single-particle density, and the occupancies of natural orbitals. Our numerical calculation allows us to explore the behavior of these observables in the transient regime of the expansion, where they are non-trivially affected by the particle interactions. We derive analytically (by using the stationary phase approximation) the formula which connects the asymptotic shape of the momentum distribution and the initial state. For sufficiently large times the momentum distribution coincides (up to a simple scaling transformation) with the shape of the real-space single-particle density (the expansion is asymptotically ballistic). Our analytical and numerical results are in good agreement.
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Empirical Formula of the Absolute Value of Electrical Conductivity for Elemental Metals and Its Interpretation By Fluctuation Dissipation Theorem: The absolute value of the electrical conductivity sigma of elemental metals even at the room temperature range is not well theoretically understood. This is particularly true in multivalent metals. This paper empirically found that sigma=n_{atom}e^2tau0/mG with tau0=hbar/k_{B}T reproduces the observations rather well for many metals as in Fig.1(b)-upper, if G is taken, by guessing to be a summed number of electric bands counted from outer most orbitals. We find by comparative study at the same time n_{atom}=n, namely Z=1 and m=m^* for majority of metals for sigma. Thus the only quantity remained is tau. The Bardeen's tau is found equal to tau0 if the deformation potential is equal to Fermi energy, using the observationally ascertained fact that thermal acoustic energy=the Fermi energy. Since electrons behave nearly as free electrons, the wave function should show the minimum uncertainty relation of Delta p_{x} Delta_{x}=hbar/2, which following the classical Fluctuation-Dissipation-Theorem shows in fact tau0=hbar/k_{B}T.
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On Entropy Wind in Superfluid Helium: Generation of a quasi-stationary flow of the superfluid helium normal part in the presence of intense first- and second-sound waves is studied. Relevant equations are obtained. The contribution to the process of energy dissipation at the shock front layer and of fluid viscosity is analysed in detail for the case of a second-sound wave. An estimate concerning possible experimental observation of the process is made.
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Magnetic vortex nucleation/annihilation in artificial-ferrimagnet microdisks: The topological nature of magnetic-vortex state gives rise to peculiar magnetization reversal observed in magnetic microdisks. Interestingly, magnetostatic and exchange energies which drive this reversal can be effectively controlled in artificial ferrimagnet heterostructures composed of rare-earth and transition metals. 25x[Py(t)/Gd(t)] (t=1 or 2 nm) superlattices demonstrate a pronounced change of the magnetization and exchange stiffness in a 10-300 K temperature range as well as very small magnetic anisotropy. Due to these properties, the magnetization of cylindrical microdisks composed of these artificial ferrimagnets can be transformed from the vortex to uniformly-magnetized states in a permanent magnetic field by changing the temperature. We explored the behavior of magnetization in 1.5-micrometer 25x[Py(t)/Gd(t)] (t=1 or 2 nm) disks at different temperatures and magnetic fields and observed that due to the energy barrier separating vortex and uniformly-magnetized states, the vortex nucleation and annihilation occur at different temperatures. This causes the temperature dependences of the Py/Gd disks magnetization to demonstrate unique hysteretic behavior in a narrow temperature range. It was discovered that for the 25x[Py(2 nm)/Gd(2 nm)] microdisks the vortex can be metastable at a certain temperature range.
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Experimental determination of the dipolar field in Mn12-acetate: Crystals of the molecular magnet Mn12-acetate are known to contain a small fraction of low- symmetry (minor) species with a small anisotropy barrier against spin reversal. The lower barrier leads to faster magnetic relaxation and lower coercive field. We exploit the low coercive fields of the minor species to make a direct determination of the dipole field in Mn12-ac. We find that the dipolar field of a fully magnetized crystal is 51.5 \pm 8.5 mT, consistent with theoretical expectations.
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NMR in $^3$He-B: This text contains a collection of equations useful for understanding Nuclear Magnetic Resonance (NMR) experiments in superfluid $^3$He-B. This is a part of my notebook where I try to describe some parts of this sophisticated system.
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Propagation of self-localised Q-ball solitons in the $^3$He universe: In relativistic quantum field theories, compact objects of interacting bosons can become stable owing to conservation of an additive quantum number $Q$. Discovering such $Q$-balls propagating in the Universe would confirm supersymmetric extensions of the standard model and may shed light on the mysteries of dark matter, but no unambiguous experimental evidence exists. We report observation of a propagating long-lived $Q$-ball in superfluid $^3$He, where the role of $Q$-ball is played by a Bose-Einstein condensate of magnon quasiparticles. We achieve accurate representation of the $Q$-ball Hamiltonian using the influence of the number of magnons, corresponding to the charge $Q$, on the orbital structure of the superfluid $^3$He order parameter. This realisation supports multiple coexisting $Q$-balls which in future allows studies of $Q$-ball dynamics, interactions, and collisions.
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Stroboscopic aliasing in long-range interacting quantum systems: We unveil a mechanism for generating oscillations with arbitrary multiplets of the period of a given external drive, in long-range interacting quantum many-particle spin systems. These oscillations break discrete time translation symmetry as in time crystals, but they are understood via two intertwined stroboscopic effects similar to the aliasing resulting from video taping a single fast rotating helicopter blade. The first effect is similar to a single blade appearing as multiple blades due to a frame rate that is in resonance with the frequency of the helicopter blades' rotation; the second is akin to the optical appearance of the helicopter blades moving in reverse direction. Analogously to other dynamically stabilized states in interacting quantum many-body systems, this stroboscopic aliasing is robust to detuning and excursions from a chosen set of driving parameters, and it offers a novel route for engineering dynamical $n$-tuplets in long-range quantum simulators, with potential applications to spin squeezing generation and entangled state preparation.
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Excitons in long molecular chains near the reflecting interface: We discuss coherent exciton-polariton states in long molecular chains that are formed due to the interaction of molecular excitations with both vacuum photons and surface excitations of the neighboring reflecting substrate. The resonance coupling with surface plasmons (or surface polaritons) of the substrate can substantially contribute to the retarded intermolecular interactions leading to an efficient channel of the decay of one-dimensional excitons with small momenta via emission of surface excitations. The interface also modifies the radiative decay of excitons into vacuum photons. In an idealized system, excitons with higher momenta would not emit photons nor surface waves. For a dissipative substrate, additional exciton quenching takes place owing to Joule losses as the electric field of the exciton polarization penetrates the substrate. We discuss how these effects depend on the polarization of molecular excitations, their frequency and on the distance of the chain from the substrate.
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Electronic properties of ordered and disordered linear clusters of atoms and molecules: The electronic properties of one-dimensional clusters of N atoms or molecules have been studied. The model used is similar to the Kronig-Penney model with the potential offered by each ion being approximated by an attractive delta function. The energy eigenvalues, the eigenstates and the density of states are calculated exactly for a linear cluster of N atoms or molecules. The dependence of these quantities on the various parameters of the problem show interesting behavior. Effects of random distribution of the positions of the atoms and random distribution of the strengths of the potential have also been studied. The results obtained in this paper can have direct applications for linear chain of atoms produced on metal surfaces or artificially created chain of atoms by using scanning tunneling microscope or in studying molecular conduction of electrons across one-dimensional barriers.
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Thermodynamically consistent equilibrium properties of normal-liquid Helium-3: The high-precision data for the specific heat C_{V}(T,V) of normal-liquid Helium-3 obtained by Greywall, taken together with the molar volume V(T_0,P) at one temperature T_0, are shown to contain the complete thermodynamic information about this phase in zero magnetic field. This enables us to calculate the T and P dependence of all equilibrium properties of normal-liquid Helium-3 in a thermodynamically consistent way for a wide range of parameters. The results for the entropy S(T,P), specific heat at constant pressure C_P(T,P), molar volume V(T,P), compressibility kappa(T,P), and thermal expansion coefficient alpha(T,P) are collected in the form of figures and tables. This provides the first complete set of thermodynamically consistent values of the equilibrium quantities of normal-liquid Helium-3. We find, for example, that alpha(T,P) has a surprisingly intricate pressure dependence at low temperatures, and that the curves alpha(T,P) vs T do not cross at one single temperature for all pressures, in contrast to the curves presented in the comprehensive survey of helium by Wilks. Corrected in cond-mat/9906222v3: The sign of the coefficient d_0 was misprinted in Table I of cond-mat/9906222v1 and v2. It now correctly reads d_0=-7.1613436. All results in the paper were obtained with the correct value of d_0. (We would like to thank for E. Collin, H. Godfrin, and Y. Bunkov for finding this misprint.)
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Three comments on the Fermi gas at unitarity in a harmonic trap: In this note we consider three issues related to the unitary Fermi gas in a harmonic trap. We present a short proof of a virial theorem, which states that the average energy of a particle system at unitarity in a harmonic trap is twice larger than the average potential energy. The theorem is valid for all systems with no intrinsic scale, at zero or finite temperature. We discuss the odd-even splitting in a unitarity Fermi gas in a harmonic trap. We show that at large number of particles N the odd-even splitting is proportional to N^{1/9}\hbar\omega, with an undetermined numerical constant. We also show that for odd N the lowest excitation energies are of order N^{-1/3}\hbar\omega.
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Measurements on Melting Pressure, Metastable Solid Phases, and Molar Volume of Univariant Saturated Helium Mixture: A concentration-saturated helium mixture at the melting pressure consists of two liquid phases and one or two solid phases. The equilibrium system is univariant, whose properties depend uniquely on temperature. Four coexisting phases can exist on singular points, which are called quadruple points. As a univariant system, the melting pressure could be used as a thermometric standard. It would provide some advantages compared to the current reference, namely pure $^3$He, especially at the lowest temperatures below 1 mK. We have extended the melting pressure measurements of the concentration-saturated helium mixture from 10 mK to 460 mK. The density of the dilute liquid phase was also recorded. The effect of the equilibrium crystal structure changing from hcp to bcc was clearly seen at T=294 mK at the melting pressure P=2.638 MPa. We observed the existence of metastable solid phases around this point. No evidence was found for the presence of another, disputed, quadruple point at around 400 mK. The experimental results agree well with our previous calculations at low temperatures, but deviate above 200 mK.
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Theory of Forces Induced by Evanescent Fields: We present the theoretical foundations of the interaction of electromagnetic evanescent fields on an object
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Anomalous Hall conductivity: local orbitals approach: A theory of the anomalous Hall conductivity based on the properties of single site orbitals is presented. Effect of the finite electron life time is modeled by energy fluctuations of atomic-like orbitals. Transition from the ideal Bloch system for which the conductivity is determined by the Berry phase curvatures to the case of strong disorder for which the conductivity becomes dependent on the relaxation time is analyzed. Presented tight-binding model gives by the unified way experimentally observed qualitative features of the anomalous conductivity in the so called good metal regime and that called as bad metal or hopping regime.
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Photon transport in a dissipative chain of nonlinear cavities: We analyze a chain of coupled nonlinear optical cavities driven by a coherent source of light localized at one end and subject to uniform dissipation. We characterize photon transport by studying the populations and the photon correlations as a function of position. When complemented with input-output theory, these quantities provide direct information about photon transmission through the system. The position of single- and multi-photon resonances directly reflect the structure of the many-body energy levels. This shows how a study of transport along a coupled cavity array can provide rich information about the strongly correlated (many-body) states of light even in presence of dissipation. By means of a numerical algorithm based on the time-evolving block decimation scheme adapted to mixed states, we are able to simulate arrays up to sixty cavities.
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The Effect Of Delay Times On The Optimal Velocity Traffic Flow Behavior: We have numerically investigated the effect of the delay times $\tau_f$ and $\tau_s$ of a mixture of fast and slow vehicles on the fundamental diagram of the optimal velocity model. The optimal velocity function of the fast cars depends not only on the headway of each car but also on the headway of the immediately preceding one. It is found that the small delay times have almost no effects, while, for sufficiently large delay time $\tau_s$ the current profile displays qualitatively five different forms depending on $\tau_f$, $\tau_s$ and the fractions $d_f$ and $d_s$ of the fast and slow cars respectively. The velocity (current) exhibits first order transitions at low and/or high densities, from freely moving phase to the congested state, and from congested state to the jamming one respectively accompanied by the existence of a local minimal current. Furthermore, there exist a critical value of $\tau_f$ above which the metastability and hysteresis appear. The spatial-temporal traffic patterns present more complex structure
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Generalized Mean Field Approach to a Resonant Bose-Fermi Mixture: We formulate a generalized mean-field theory of a mixture of fermionic and bosonic atoms, in which the fermion-boson interaction can be controlled by a Feshbach resonance. The theory correctly accounts for molecular binding energies of the molecules in the two-body limit, in contrast to the most straightforward mean-field theory. Using this theory, we discuss the equilibrium properties of fermionic molecules created from atom pairs in the gas. We also address the formation of molecules when the magnetic field is ramped across the resonance, and present a simple Landau-Zener result for this process.
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Statics and dynamics of BEC's in double square well potentials: In this paper we treat the behavior of Bose Einstein condensates in double square well potentials, both of equal and different depths. For even depth, symmetry preserving solutions to the relevant nonlinear Schr\"{o}dinger equation is known, just as in the linear limit. When the nonlinearity is strong enough, symmetry breaking solutions also exist, side by side with the symmetric one. Interestingly, solutions almost entirely localized in one of the wells are known as an extreme case. Here we outline a method for obtaining all these solutions for repulsive interactions. The bifurcation point at which, for critical nonlinearity, the asymmetric solutions branch off from the symmetry preserving ones is found analytically. We also find this bifurcation point and treat the solutions generally via a Josephson Junction model. When the confining potential is in the form of two wells of different depth, interesting new phenomena appear. This is true of both the occurrence of the bifurcation point for the static solutions, and also of the dynamics of phase and amplitude varying solutions. Again a generalization of the Josephson model proves useful. The stability of solutions is treated briefly.
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Dynamical instability and domain formation in a spin-1 Bose condensate: We interpret the recently observed spatial domain formation in spin-1 atomic condensates as a result of dynamical instability. Within the mean field theory, a homogeneous condensate is dynamically unstable (stable) for ferromagnetic (antiferromagnetic) atomic interactions. We find this dynamical instability naturally leads to spontaneous domain formation as observed in several recent experiments for condensates with rather small numbers of atoms. For trapped condensates, our numerical simulations compare quantitatively to the experimental results, thus largely confirming the physical insight from our analysis of the homogeneous case.
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Classical and quantum dynamics of a model for atomic-molecular Bose--Einstein condensates: We study a model for a two-mode atomic-molecular Bose--Einstein condensate. Starting with a classical analysis we determine the phase space fixed points of the system. It is found that bifurcations of the fixed points naturally separate the coupling parameter space into four regions. The different regions give rise to qualitatively different dynamics. We then show that this classification holds true for the quantum dynamics.
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Modelling turbulent flow of superfluid $^4$He past a rough solid wall in the $T = 0$ limit: We present a numerical study, using the vortex filament model, of vortex tangles in a flow of pure superfluid $^4$He in the $T = 0$ limit through a channel of width $D = 1$ mm for various applied velocities $V$. The flat channel walls are assumed to be microscopically rough such that vortices terminating at the walls are permanently pinned; vortices are liberated from their pinned ends exclusively through self-reconnection with their images. Sustained tangles were observed, for a period of 80 s, above the critical velocity $V_c \sim 0.20$ cm s$^{-1} = 20 \kappa/D$. The coarse-grained velocity profile was akin to a classical parabolic profile of the laminar Poiseuille flow, albeit with a non-zero slip velocity $\sim$ 0.20 cm s$^{-1}$ at the walls. The friction force was found to be proportional to the applied velocity. The effective kinematic viscosity was $\sim 0.1\kappa$, and effective Reynolds numbers within $\mathrm{Re'} < 15$. The fraction of the polarized vortex length varied between zero in the middle of the channel and $\sim$ 60% within the shear flow regions $\sim D/4$ from the walls. Therefore, we studied a state of polarized ultraquantum (Vinen) turbulence fuelled at short lengthscales by vortex reconnections, including those with vortex images due to the relative motion between the vortex tangle and the pinning rough surface.
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Scanning optical homodyne detection of high-frequency picoscale resonances in cantilever and tuning fork sensors: Higher harmonic modes in nanoscale silicon cantilevers and microscale quartz tuning forks are detected and characterized using a custom scanning optical homodyne interferometer. Capable of both mass and force sensing, these resonators exhibit high-frequency harmonic motion content with picometer-scale amplitudes detected in a 2.5 MHz bandwidth, driven by ambient thermal radiation. Quartz tuning forks additionally display both in-plane and out-of-plane harmonics. The first six electronically detected resonances are matched to optically detected and mapped fork eigenmodes. Mass sensing experiments utilizing higher tuning fork modes indicate >6x sensitivity enhancement over fundamental mode operation.
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A model for luminescence of localized state ensemble: A distribution function for localized carriers, $f(E,T)=\frac{1}{e^{(E-E_a)/k_BT}+\tau_{tr}/\tau_r}$, is proposed by solving a rate equation, in which, electrical carriers' generation, thermal escape, recapture and radiative recombination are taken into account. Based on this distribution function, a model is developed for luminescence from localized state ensemble with a Gaussian-type density of states. The model reproduces quantitatively all the anomalous temperature behaviors of localized state luminescence. It reduces to the well-known band-tail and luminescence quenching models under certain approximations.
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The constitutive tensor of linear elasticity: its decompositions, Cauchy relations, null Lagrangians, and wave propagation: In linear anisotropic elasticity, the elastic properties of a medium are described by the fourth rank elasticity tensor C. The decomposition of C into a partially symmetric tensor M and a partially antisymmetric tensors N is often used in the literature. An alternative, less well-known decomposition, into the completely symmetric part S of C plus the reminder A, turns out to be irreducible under the 3-dimensional general linear group. We show that the SA-decomposition is unique, irreducible, and preserves the symmetries of the elasticity tensor. The MN-decomposition fails to have these desirable properties and is such inferior from a physical point of view. Various applications of the SA-decomposition are discussed: the Cauchy relations (vanishing of A), the non-existence of elastic null Lagrangians, the decomposition of the elastic energy and of the acoustic wave propagation. The acoustic or Christoffel tensor is split in a Cauchy and a non-Cauchy part. The Cauchy part governs the longitudinal wave propagation. We provide explicit examples of the effectiveness of the SA-decomposition. A complete class of anisotropic media is proposed that allows pure polarizations in arbitrary directions, similarly as in an isotropic medium.
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Transmodal Fabry-Pérot Resonance: Theory and Realization with Elastic Metamaterials: We discovered a new transmodal Fabry-P\'erot resonance that one elastic-wave mode is maximally transmitted to another when the phase difference of two dissimilar modes through an anisotropic layer is exactly odd multiples of {\pi}. Unlike the well-established Fabry-P\'erot resonance, the transmodal resonance must involve two coupled elastic-wave modes, longitudinal and shear. The formation of wiggly transmodal transmission spectra is due to structural instability appearing in anisotropic mode-coupled elastic-media. Experiments with elastic metamaterials confirmed our findings which can play a critical role in shear-mode ultrasound applications.
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A priori Wannier functions from modified Hartree-Fock and Kohn-Sham equations: The Hartree-Fock equations are modified to directly yield Wannier functions following a proposal of Shukla et al. [Chem. Phys. Lett. 262, 213-218 (1996)]. This approach circumvents the a posteriori application of the Wannier transformation to Bloch functions. I give a novel and rigorous derivation of the relevant equations by introducing an orthogonalizing potential to ensure the orthogonality among the resulting functions. The properties of these, so-called a priori Wannier functions, are analyzed and the relation of the modified Hartree-Fock equations to the conventional, Bloch-function-based equations is elucidated. It is pointed out that the modified equations offer a different route to maximally localized Wannier functions. Their computational solution is found to involve an effort that is comparable to the effort for the solution of the conventional equations. Above all, I show how a priori Wannier functions can be obtained by a modification of the Kohn-Sham equations of density-functional theory.
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Threshold for Chaos and Thermalization in One-Dimensional Mean-Field Bose-Hubbard Model: We study the threshold for chaos and its relation to thermalization in the 1D mean-field Bose-Hubbard model, which in particular describes atoms in optical lattices. We identify the threshold for chaos, which is finite in the thermodynamic limit, and show that it is indeed a precursor of thermalization. Far above the threshold, the state of the system after relaxation is governed by the usual laws of statistical mechanics.
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Thermodynamic Measurements in a Strongly Interacting Fermi Gas: We conduct a series of measurements on the thermodynamic properties of an optically-trapped strongly interacting Fermi gas, including the energy $E$, entropy $S$, and sound velocity $c$. Our model-independent measurements of $E$ and $S$ enable a precision study of the finite temperature thermodynamics. The $E(S)$ data are directly compared to several recent predictions. The temperature in both the superfluid and normal fluid regime is obtained from the fundamental thermodynamic relation $T=\partial E/\partial S$ by parameterizing the $E(S)$ data. Our $E(S)$ data are also used to experimentally calibrate the endpoint temperatures obtained for adiabatic sweeps of the magnetic field between the ideal and strongly interacting regimes. This enables the first experimental calibration of the temperature scale used in experiments on fermionic pair condensation. Our calibration shows that the ideal gas temperature measured for the onset of pair condensation corresponds closely to the critical temperature estimated in the strongly interacting regime from the fits to our $E(S)$ data. The results are in very good agreement with recent predictions. Finally, using universal thermodynamic relations, we estimate the chemical potential and heat capacity of the trapped gas from the $E(S)$ data.
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Shear-strain-induced Spatially Varying Super-lattice Structures on Graphite studied by STM: We report on the Scanning Tunneling Microscope (STM) observation of linear fringes together with spatially varying super-lattice structures on (0001) graphite (HOPG) surface. The structure, present in a region of a layer bounded by two straight carbon fibers, varies from a hexagonal lattice of 6nm periodicity to nearly a square lattice of 13nm periodicity. It then changes into a one-dimensional (1-D) fringe-like pattern before relaxing into a pattern-free region. We attribute this surface structure to a shear strain giving rise to a spatially varying rotation of the affected graphite layer relative to the bulk substrate. We propose a simple method to understand these moire patterns by looking at the fixed and rotated lattices in the Fourier transformed k-space. Using this approach we can reproduce the spatially varying 2-D lattice as well as the 1-D fringes by simulation. The 1-D fringes are found to result from a particular spatial dependence of the rotation angle.
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Highly sensitive and broadband carbon nanotube radio-frequency single-electron transistor: We have investigated radio-frequency single-electron transistor (RF-SET) operation of single-walled carbon nanotube quantum dots in the strong tunneling regime. At 4.2 K and carrier frequency 754.2 MHz, we reach a charge sensitivity of 2.3e-6 e/Hz^(1/2) over a bandwidth of 85 MHz. Our results indicate a gain-bandwidth product of 3.7e13 Hz^(3/2)/e, which is by one order of magnitude better than for typical RF-SETs.
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Counterflow quantum turbulence in a square channel under the normal fluid with a Poiseuille flow: We perform a numerical analysis of superfluid turbulence produced by thermal counterflow in He II by using the vortex filament model. Counterflow in a low aspect ratio channel is known to show the transition from laminar flow to the two turbulent states TI and TII. The present understanding is that the TI has the turbulent superfluid and the laminar normal fluid but both fluids are turbulent in the TII state. This work studies the vortex tangle in the TI state. Solid boundary condition is applied to walls of a square channel, and the velocity field of the normal fluid is prescribed to be a laminar Poiseuille profile. An inhomogeneous vortex tangle, which concentrates near the solid boundaries, is obtained as the statistically steady state. It is sustained by its characteristic space-time oscillation. The inhomogeneity of the vortex tangle shows the characteristic dependence on temperature, which is caused by two competitive effects, namely the profile of the counterflow velocity and the mutual friction.
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A new ripplon branch in He II: We analyse the dispersion relation of ripplons, on the surface of superfluid helium, using the dispersive hydrodynamics approach and find a new ripplon branch. We obtain analytical equation for the dispersion relation and analytic expressions for the limiting cases. We discuss where ripplons can exist in the energy-wavenumber plane. A numerical solution for the ripplon dispersion curve is obtained in the allowed regions. The new ripplon branch is found at energies just below the instability point.
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Strong magnetic coupling between an electronic spin qubit and a mechanical resonator: We describe a technique that enables a strong, coherent coupling between a single electronic spin qubit associated with a nitrogen-vacancy impurity in diamond and the quantized motion of a magnetized nano-mechanical resonator tip. This coupling is achieved via careful preparation of dressed spin states which are highly sensitive to the motion of the resonator but insensitive to perturbations from the nuclear spin bath. In combination with optical pumping techniques, the coherent exchange between spin and motional excitations enables ground state cooling and the controlled generation of arbitrary quantum superpositions of resonator states. Optical spin readout techniques provide a general measurement toolbox for the resonator with quantum limited precision.
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The cold atom Hubbard toolbox: We review recent theoretical advances in cold atom physics concentrating on strongly correlated cold atoms in optical lattices. We discuss recently developed quantum optical tools for manipulating atoms and show how they can be used to realize a wide range of many body Hamiltonians. Then we describe connections and differences to condensed matter physics and present applications in the fields of quantum computing and quantum simulations. Finally we explain how defects and atomic quantum dots can be introduced in a controlled way in optical lattice systems.
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Higher-order vortex solitons, multipoles, and supervortices on a square optical lattice: We predict new generic types of vorticity-carrying soliton complexes in a class of physical systems including an attractive Bose-Einstein condensate in a square optical lattice (OL) and photonic lattices in photorefractive media. The patterns include ring-shaped higher-order vortex solitons and supervortices. Stability diagrams for these patterns, based on direct simulations, are presented. The vortex ring solitons are stable if the phase difference \Delta \phi between adjacent solitons in the ring is larger than \pi/2, while the supervortices are stable in the opposite case, \Delta \phi <\pi /2. A qualitative explanation to the stability is given.
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Bose-Einstein condensate in a quartic potential: Static and Dynamic properties: In this paper, we present a theoretical study of a Bose-Einstein condensate of interacting bosons in a quartic trap in one, two, and three dimensions. Using Thomas-Fermi approximation, suitably complemented by numerical solutions of the Gross-Pitaevskii equation, we study the ground sate condensate density profiles, the chemical potential, the effects of cross-terms in the quartic potential, temporal evolution of various energy components of the condensate, and width oscillations of the condensate. Results obtained are compared with corresponding results for a bose condensate in a harmonic confinement.
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Optical Tamm states in one-dimensional magnetophotonic structures: We demonstrate the existence of a spectrally narrow localized surface state, the so-called optical Tamm state, at the interface between a 1D magnetophotonic and non-magnetic photonic crystals. The state is spectrally located inside the photonic band gaps of each of the photonic crystals comprising this magnetophotonic structure. This state is associated with a sharp transmission peak through the sample and is responsible for the substantial enhancement of the Faraday rotation for the corresponding wavelength. The experimental results are in excellent agreement with the theoretical predictions.
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Quasiparticle universes in Bose-Einstein condensates: Recent developments in simulating fundamental quantum field theoretical effects in the kinematical context of analogue gravity are reviewed. Specifically, it is argued that a curved space-time generalization of the Unruh-Davies effect -- the Gibbons-Hawking effect in the de Sitter space-time of inflationary cosmological models -- can be implemented and verified in an ultracold gas of bosonic atoms.
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Evaporative Cooling of a Photon Fluid to Quantum Degeneracy: We demonstrate that the process of evaporative cooling, as associated with the cooling of atomic gases, can also be employed to condense a system of photons giving rise to coherent properties of the light. The system we study consists of photons in a high-quality Fabry-Perot cavity with photon interactions mediated by a nonlinear atomic medium. We predict a macroscopic occupation of the lowest energy mode and evaluate the conditions for realizing a narrow spectral width indicative of a long coherence time for the field.
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Entangling two defects via a surrounding crystal: We theoretically show how two impurity defects in a crystalline structure can be entangled through coupling with the crystal. We demonstrate this with a harmonic chain of trapped ions in which two ions of a different species are embedded. Entanglement is found for sufficiently cold chains and for a certain class of initial, separable states of the defects. It results from the interplay between localized modes which involve the defects and the interposed ions, it is independent of the chain size, and decays slowly with the distance between the impurities. These dynamics can be observed in systems exhibiting spatial order, viable realizations are optical lattices, optomechanical systems, or cavity arrays in circuit QED.
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Quantum oscillations in a two-mode atom-molecule Bose-Einstein condensate -- the discrete WKB approach: Quantum effects in a system of coupled atomic and molecular Bose-Einstein condensates in the framework of a two-mode model are studied numerically and analytically, using the discrete WKB approach. In contrast to the mean-field approximation, the WKB analytical results are in a very good agreement with numerical results. The quantum fluctuations of the atomic and molecular populations are calculated, and found to be of the same order of magnitude as their mean values.
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Radial quadrupole and scissors modes in trapped Fermi gases across the BCS phase transition: The excitation spectra of the radial quadrupole and scissors modes of ultracold Fermi gases in elongated traps are studied across the BCS superfluid-normal phase transition in the framework of a transport theory for quasiparticles. In the limit of zero temperature, this theory reproduces the results of superfluid hydrodynamics, while in the opposite limit, above the critical temperature, it reduces to the collisionless Vlasov equation. In the intermediate temperature range, the excitation spectra have two or three broad peaks, respectively, which are roughly situated at hydrodynamic and collisionless frequencies, and whose strength is shifted from the hydrodynamic to the collisionless modes with increasing temperature. By fitting the time dependent quadrupole deformation with a damped oscillation of a single frequency, we can understand the "jump" of the frequency of the radial quadrupole mode as a function of interaction strength which has recently been reported by the Innsbruck group.
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Hall Viscosity and the Acoustic Faraday Effect: For more than 20 years, observation of the non-dissipative Hall viscosity in the quantum Hall effect has been impeded by the difficulty to probe directly the momentum of the two-dimensional electron gas. However, in three-dimensional systems such as superfluid ${}^{3}\mathrm{He}\!\!-\!\!\mathrm{B}$, the momentum density is readily probed through transverse acoustic waves. We show that in a three-dimensional elastic medium supporting transverse waves, a non-vanishing Hall viscosity induces circular birefringence. Such an effect has been observed in ${}^{3}\mathrm{He}\!\!-\!\!\mathrm{B}$ in the presence of a weak magnetic field, and is known as the acoustic Faraday effect. The acoustic Faraday effect has been understood in terms of the Zeeman splitting of the excited order parameter modes which support the transverse wave propagation in the superfluid. We show that the Zeeman effect can generically lead to a non-zero Hall viscosity coefficient, and confirm this prediction using a simple phenomenological model for the ${}^{3}\mathrm{He}\!\!-\!\!\mathrm{B}$ collective modes. Therefore, we claim that the observation of the acoustic Faraday effect can be leveraged to make a direct observation of the Hall viscosity in superfluid ${}^{3}\mathrm{He}\!\!-\!\!\mathrm{B}$ in a magnetic field and other systems such as the crystalline $\mathrm{Tb}_{3}\mathrm{Ga}_{5}\mathrm{O}_{12}$ material.
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A simple model of Feshbach molecules: We present a two-channel model to describe the quantum state of two atoms with finite-range interaction near a Feshbach resonance. This model provides a simple picture to analytically derive the wave function and the binding energy of the molecular bound state. The results agree excellently with the measurements and multichannel calculations. For small binding energies, the system enters a threshold regime in which the Feshbach molecules are identical to long range atom pairs in single channel. According to their threshold behavior, we find Feshbach resonances can be classified into two types.
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N-particle Bogoliubov vacuum state: We consider the Bogoliubov vacuum state in the number-conserving Bogoliubov theory proposed by Castin and Dum [Phys. Rev. A 57, 3008 (1998)]. We show that in the particle representation the vacuum can be written in a simple diagonal form. The vacuum state can describe the stationary N-particle ground state of a condensate in a trap, but it can also represent a dynamical state when, for example, a Bose-Einstein condensate initially prepared in the stationary ground state is subject to a time-dependent perturbation. In both cases the diagonal form of the Bogoliubov vacuum can be obtained by basically diagonalizing the reduced single particle density matrix of the vacuum. We compare N-body states obtained within the Bogoliubov theory with the exact ground states in a 3-site Bose-Hubbard model. In this example, the Bogoliubov theory fails to accurately describe the stationary ground state in the limit when N goes to infinity but a small fraction of depleted particles is kept constant.
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A simple variational approach for an interacting Fermi trapped gas: Quantum states of a two-component Fermi trapped gas are described by introducing an effective trap frequency, determined via variational techniques. Closed expressions for the contribution of a contact interaction potential to the total energy and the pairing interaction are derived. They are valid for both few and large number of particles, given the discrete nature of the formulation, and therefore richer than the continuous expressions, which are perfectly matched. Pairing energies within a shell are explicitly evaluated and its allowed values at a given energy level delimited. We show the importance of the interaction over the trap energy as the number of particles ($N$) grows and the temperature decreases. At zero temperature we find a polynomial dependence of the interaction energy on the Fermi energy, whose dominant term at large $N$ corresponds with the mean field approximation result. In addition, the role of the strength of an attractive potential on the total energy is exhibited.
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Implications of experimental probes of the RG-flow in quantum Hall systems: We review the implications of the scaling data for the emergent symmetry of the quantum Hall system. The location of the fixed points in the conductivity plane is consistent with the global, non-Abelian discrete symmetry $\Gamma _{0}(2)$, and the renormalisation group (RG) flow-lines agree closely with that found if the symmetry acts anti-holomorphically. We extend the analysis to consider the rate of the RG flow. For a specific model in which the $\Gamma _{0}(2)$ symmetry acts anti-holomorphically the scaling close to the fixed points gives a critical delocalisation exponent $\nu = 2.38\pm 0.02$, in excellent greement with direct measurements and with numerical simulations. Both the predicted flow-lines and the flow rate also agree with the experimental measurements far away from the critical points, suggesting an emergent topological structure capable of stabilising the symmetry predictions. We hope that this agreement will stimulate further experimental study capable of conclusively testing the symmetry and exploring its associated dynamics.
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Entangling two defects via a surrounding crystal: We theoretically show how two impurity defects in a crystalline structure can be entangled through coupling with the crystal. We demonstrate this with a harmonic chain of trapped ions in which two ions of a different species are embedded. Entanglement is found for sufficiently cold chains and for a certain class of initial, separable states of the defects. It results from the interplay between localized modes which involve the defects and the interposed ions, it is independent of the chain size, and decays slowly with the distance between the impurities. These dynamics can be observed in systems exhibiting spatial order, viable realizations are optical lattices, optomechanical systems, or cavity arrays in circuit QED.
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Sound velocities of hexagonal close-packed H2 and He under pressure: Bulk, shear, and compressional aggregate sound velocities of hydrogen and helium in the close- packed hexagonal structure are calculated over a wide pressure range using two complementary approaches: semi-empirical lattice dynamics based on the many-body intermolecular potentials and density-functional theory in the generalized gradient approximation. The sound velocities are used to calculate pressure dependence of the Debye temperature. The comparison between experiment and first-principle and semi-empirical calculations provide constraints on the density dependence of intermolecular interactions in the zero-temperature limit.
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Nuclear Spin Relaxation of Very Dilute 3He impurities in Solid 4He: We report measurements of the nuclear spin-lattice and spin-spin relaxation times of very dilute 3He in solid 4He in the temperature range 0.01 \leq T \leq 0.5 K for densities where anomalies have been observed in torsional oscillator and shear modulus measurements. We compare the results with the values of the relaxation times reported by other observers for higher concentrations and the theory of Landesman that takes into account the elastic properties of the 4He lattice. A sharp increase in the magnitude of the nuclear spin-lattice relaxation times compared to the the classical Landesman theory is observed close to the temperatures where the torsional and shear modulus anomalies are observed. The NMR results suggest that the tunneling of 3He impurities in the atomic-scale elastic distortion is affected by the same processes that give rise to the macroscopic elastic dissipation anomalies.
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Ultrastrong coupling between a cavity resonator and the cyclotron transition of a 2D electron gas in the case of integer filling factor: We investigate theoretically the coupling between a cavity resonator and the cyclotron transition of a two dimensional electron gas under an applied perpendicular magnetic field. We derive and diagonalize an effective quantum Hamiltonian describing the magnetopolariton excitations of the two dimensional electron gas for the case of integer filling factors. The limits of validity of the present approach are critically discussed. The dimensionless vacuum Rabi frequency $\Omega_0/\omega_0$ (i.e., normalized to the cyclotron frequency $\omega_0$) is shown to scale as $\sqrt{\alpha\: n_{QW} \nu}$, where $\alpha$ is the fine structure constant, $n_{QW}$ is the number of quantum wells and $\nu$ is the filling factor in each well. We show that with realistic parameters of a high-mobility semiconductor two dimensional electron gas, the dimensionless coupling $\Omega_0/\omega_0$ can be much larger than 1 in the case of $\nu \gg 1$, the latter condition being typically realized for cyclotron transitions in the microwave range. Implications of such ultrastrong coupling regime are discussed.
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Dissipation-managed soliton in a quasi-one-dimensional Bose-Einstein condensate: We use the time-dependent mean-field Gross-Pitaevskii equation to study the formation of a dynamically-stabilized dissipation-managed bright soliton in a quasi-one-dimensional Bose-Einstein condensate (BEC). Because of three-body recombination of bosonic atoms to molecules, atoms are lost (dissipated) from a BEC. Such dissipation leads to the decay of a BEC soliton. We demonstrate by a perturbation procedure that an alimentation of atoms from an external source to the BEC may compensate for the dissipation loss and lead to a dynamically-stabilized soliton. The result of the analytical perturbation method is in excellent agreement with mean-field numerics. It seems possible to obtain such a dynamically-stabilized BEC soliton without dissipation in laboratory.
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Influence of structure on the optical limiting properties of nanotubes: We investigate the role of carbon nanotubes structure on their optical limiting properties. Samples of different and well-characterized structural features are studied by optical limiting and pump-probe experiments. The influence of the diameter's size on the nano-object is demonstrated. Indeed, both nucleation and growth of gas bubbles are expected to be sensitive to diameter.
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The Boron Buckyball has an Unexpected Th Symmetry: The boron buckyball avoids the high symmetry icosahedral cage structure. The previously reported Ih symmetric structure is not an energy minimum in the potential energy surface and exhibits a spontaneous symmetry breaking to yield a puckered cage with a rare Th symmetry. The HOMO-LUMO gap is twice as large as the reported value and amounts to 1.94 eV at B3LYP/6-31G(d) level. The valence orbital structure of boron buckyball is identical to the one in the carbon analogue.
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Proton transport and torque generation in rotary biomotors: We analyze the dynamics of rotary biomotors within a simple nano-electromechanical model, consisting of a stator part and a ring-shaped rotor having twelve proton-binding sites. This model is closely related to the membrane-embedded F$_0$ motor of adenosine triphosphate (ATP) synthase, which converts the energy of the transmembrane electrochemical gradient of protons into mechanical motion of the rotor. It is shown that the Coulomb coupling between the negative charge of the empty rotor site and the positive stator charge, located near the periplasmic proton-conducting channel (proton source), plays a dominant role in the torque-generating process. When approaching the source outlet, the rotor site has a proton energy level higher than the energy level of the site, located near the cytoplasmic channel (proton drain). In the first stage of this torque-generating process, the energy of the electrochemical potential is converted into potential energy of the proton-binding sites on the rotor. Afterwards, the tangential component of the Coulomb force produces a mechanical torque. We demonstrate that, at low temperatures, the loaded motor works in the shuttling regime where the energy of the electrochemical potential is consumed without producing any unidirectional rotation. The motor switches to the torque-generating regime at high temperatures, when the Brownian ratchet mechanism turns on. In the presence of a significant external torque, created by ATP hydrolysis, the system operates as a proton pump, which translocates protons against the transmembrane potential gradient. Here we focus on the F$_0$ motor, even though our analysis is applicable to the bacterial flagellar motor.
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Experimental realities refuting the existence of p=0 condensate in a system of interacting bosons : II. Spectroscopy of embedded molecules: Experimental observation of superfluidity in a microscopic cluster, $M:(^4He)_x$, of a molecule ($M$) and $x$ number of $^4He$ atoms (with $x$ ranging from 1 to many) is qualitatively analyzed. It concludes that: (i) each $^4He$ atom in the cluster has to have non-zero momentum for its confinement to a space of size ($<$ the size of the cluster), (ii) superfluidity does not require atoms with zero momentum ($p=0$), and (iii) while all $^4He$ atoms in the cluster cease to have relative motions (hence the inter-atomic collisions), they retain a freedom to move coherently in order of their locations on a closed path around the rotor ($M$ plus few nearest $^4He$ atoms which follow the molecular rotation for their relatively strong binding with $M$). The analysis also identifies the basic arrangement of $^4He$ atoms which allows the rotor to have free rotation in the cluster.
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The role of interactions in spin-polarised atomic Fermi gases at unitarity: We study the zero temperature properties of a trapped polarized Fermi gas at unitarity by assuming phase separation between an unpolarized superfluid and a polarized normal phase. The effects of the interaction are accounted using the formalism of quasi-particles to build up the equation of state of the normal phase with the Monte Carlo results for the relevant parameters. Our predictions for the Chandrasekhar-Clogston limit of critical polarization and for the density profiles, including the density jump at the interface, are confirmed with excellent accuracy by the recent experimental results at MIT. The role of interaction on the radial width of the minority component, on the gap of the RF transition and on the spin oscillations in the normal phase is also discussed. Our analysis points out the Fermi liquid nature of these strongly interacting spin polarized configurations.
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Hybrid apparatus for Bose-Einstein condensation and cavity quantum electrodynamics: Single atom detection in quantum degenerate gases: We present and characterize an experimental system in which we achieve the integration of an ultrahigh finesse optical cavity with a Bose-Einstein condensate (BEC). The conceptually novel design of the apparatus for the production of BECs features nested vacuum chambers and an in-vacuo magnetic transport configuration. It grants large scale spatial access to the BEC for samples and probes via a modular and exchangeable "science platform". We are able to produce \87Rb condensates of five million atoms and to output couple continuous atom lasers. The cavity is mounted on the science platform on top of a vibration isolation system. The optical cavity works in the strong coupling regime of cavity quantum electrodynamics and serves as a quantum optical detector for single atoms. This system enables us to study atom optics on a single particle level and to further develop the field of quantum atom optics. We describe the technological modules and the operation of the combined BEC cavity apparatus. Its performance is characterized by single atom detection measurements for thermal and quantum degenerate atomic beams. The atom laser provides a fast and controllable supply of atoms coupling with the cavity mode and allows for an efficient study of atom field interactions in the strong coupling regime. Moreover, the high detection efficiency for quantum degenerate atoms distinguishes the cavity as a sensitive and weakly invasive probe for cold atomic clouds.
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Reduced Density Matrix Functional Theory at Finite Temperature: Theoretical Foundations: We present an ab-initio approach for grand canonical ensembles in thermal equilibrium with local or nonlocal external potentials based on the one-reduced density matrix. We show that equilibrium properties of a grand canonical ensemble are determined uniquely by the eq-1RDM and establish a variational principle for the grand potential with respect to its one-reduced density matrix. We further prove the existence of a Kohn-Sham system capable of reproducing the one-reduced density matrix of an interacting system at finite temperature. Utilizing this Kohn-Sham system as an unperturbed system, we deduce a many-body approach to iteratively construct approximations to the correlation contribution of the grand potential.
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Scaling issues for AlGaN/GaN HEMTs: performance optimization via devices geometry modelling: The potential barrier between source and gate in HEMTs and between source and channel in MOSFET controls the current output and the velocity injection of electrons in the channel [1], [2]. In non self aligned structures the electric field behavior along the channel, for fixed applied voltages, is determined by the contacts positions. Anyway, in GaAs based HEMTs, the geometry of the device appears to be not determinant for the output current due to saturation effects. On the other hand, the GaN based technology still offers the possibility to enhance devices output current handling contacts distances. In this paper we will present Monte Carlo simulations results which show how a downscaling of the Source to Gate distance could improve the device performances inducing an higher potential barrier between source and gate.
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Slow-wave effect and mode-profile matching in Photonic Crystal microcavities: Physical mechanisms involved in the light confinement in photonic crystal slab microcavities are investigated. We first present a full three-dimensional numerical study of these microcavities. Then, to gain physical insight into the confinement mechanisms, we develop a Fabry-Perot model. This model provides accurate predictions and sheds new light on the physics of light confinement. We clearly identify two mechanisms to enhance the Q factor of these microcavities. The first one consists in improving the mode-profile matching at the cavity terminations and the second one in using a slow wave in the cavity.
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Scale Separation Scheme for Simulating Superfluid Turbulence: Kelvin-Wave Cascade: A Kolmogorov-type cascade of Kelvin waves--the distortion waves on vortex lines--plays a key part in the relaxation of superfluid turbulence at low temperatures. We propose an efficient numeric scheme for simulating the Kelvin wave cascade on a single vortex line. The idea is likely to be generalizable for a full-scale simulation of different regimes of superfluid turbulence. With the new scheme, we are able to unambiguously resolve the cascade spectrum exponent, and thus to settle the controversy between recent simulations [1] and recently developed analytic theory [2]. [1] W.F. Vinen, M. Tsubota and A. Mitani, Phys. Rev. Lett. 91, 135301 (2003). [2] E.V. Kozik and B.V. Svistunov, Phys. Rev. Lett. 92, 035301 (2004).
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Equations of Two-Fluid Hydrodynamics of Superfluid Helium with the Account of Electric Fields: System of two-fluid hydrodynamics of superfluid helium with the account of electric field is obtained. These equations are obtained in kinetic approach using quasi-equilibrium distribution function of quasi-particles, which vanishs collision integral of quasi-particles, and contains dependence on electric field by means of phenomenological parameter {\alpha}. Using experimental data at temperature range of 1,4 - 2 K, where basic role plays roton hydrodynamics, the value of phenomenological parameter, is obtained.
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Collective oscillations of a quasi one dimensional Bose condensate under damping: Influence of the damping on collective oscillations of a one-dimensional trapped Bose gas in the mean field regime has been studied. Using the phenomenological damping approach developed by L.P. Pitaevskii, modified variational equations for the parameters of the condensate wave function is derived. Analytical expressions for the condensate parameters in equilibrium state have been obtained. Bistability in nonlinear oscillations of the condensate under periodic variations of the trap potential is predicted. The predictions of the modified variational approach are confirmed by full numerical simulations of the 1D GP equation with the damping.
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Comment to "Mechanism for Designing Metamaterials with a High Index of Refraction": Comment to "Mechanism for Designing Metamaterials with a High Index of Refraction" by J. T. Shen, Peter B. Catrysse and Shanhui Fan.
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Characterization of high-temperature PbTe p-n junctions prepared by thermal diffusion and by ion-implantation: We describe here the characteristics of two types of high-quality PbTe p-n-junctions, prepared in this work: (1) by thermal diffusion of In4Te3 gas (TDJ), and (2) by ion implantation (implanted junction, IJ) of In (In-IJ) and Zn (Zn-IJ). The results, as presented here, demonstrate the high quality of these PbTe diodes. Capacitance-voltage and current-voltage characteristics have been measured. The measurements were carried out over a temperature range from ~ 10 K to ~ 180 K. The latter was the highest temperature, where the diode still demonstrated rectifying properties. This maximum operating temperature is higher than any of the earlier reported results. The saturation current density, J0, in both diode types, was ~ 10^-5 A/cm2 at 80 K, while at 180 K J0 ~ 10^-1 A/cm2 in TDJ and ~ 1 A/cm2 in both ion-implanted junctions. At 80 K the reverse current started to increase markedly at a bias of ~ 400 mV for TDJ, and at ~550 mV for IJ. The ideality factor n was about 1.5-2 for both diode types at 80 K. The analysis of the C-V plots shows that the junctions in both diode types are linearly graded. The analysis of the C-V plots allows also determining the height of the junction barrier, the concentrations and the concentration gradient of the impurities, and the temperature dependence of the static dielectric constant. The zero-bias-resistance x area products (R0Ae) at 80 K are: 850 OHMcm2 for TDJ, 250 OHMcm2 for In-IJ, and ~ 80 OHMcm2 for Zn-IJ, while at 180 K R0Ae ~ 0.38 OHMcm2 for TDJ, and ~ 0.1 OHMcm2 for IJ. The estimated detectivity is: D* ~ 10^10 cmHz^(1/2)/W up to T=140 K, determined mainly by background radiation, while at T=180 K, D* decreases to 108-107 cmHz^(1/2)/W, and is determined by the Johnson noise.
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Evidence for Efimov quantum states in an ultracold gas of cesium atoms: Systems of three interacting particles are notorious for their complex physical behavior. A landmark theoretical result in few-body quantum physics is Efimov's prediction of a universal set of bound trimer states appearing for three identical bosons with a resonant two-body interaction. Counterintuitively, these states even exist in the absence of a corresponding two-body bound state. Since the formulation of Efimov's problem in the context of nuclear physics 35 years ago, it has attracted great interest in many areas of physics. However, the observation of Efimov quantum states has remained an elusive goal. Here we report the observation of an Efimov resonance in an ultracold gas of cesium atoms. The resonance occurs in the range of large negative two-body scattering lengths, arising from the coupling of three free atoms to an Efimov trimer. Experimentally, we observe its signature as a giant three-body recombination loss when the strength of the two-body interaction is varied. We also detect a minimum in the recombination loss for positive scattering lengths, indicating destructive interference of decay pathways. Our results confirm central theoretical predictions of Efimov physics and represent a starting point with which to explore the universal properties of resonantly interacting few-body systems. While Feshbach resonances have provided the key to control quantum-mechanical interactions on the two-body level, Efimov resonances connect ultracold matter to the world of few-body quantum phenomena.
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Quantum Turbulence of Bellows-Driven 4He Superflow: Decay: We report on studies of quantum turbulence with second-sound in superfluid 4He in which the turbulence is generated by the flow of the superfluid component through a wide square channel, the ends of which are plugged with sintered silver superleaks, the flow being generated by compression of a bellows. The superleaks ensure that there is no net flow of the normal fluid. In an earlier paper (Phys. Rev. B, 86, 134515 (2012)) we have shown that steady flow of this kind generates a density of vortex lines that is essentially identical with that generated by thermal counterflow, when the average relative velocity between the two fluids is the same. In this paper we report on studies of the temporal decay of the vortex-line density, observed when the bellows is stopped, and we compare the results with those obtained from the temporal decay of thermal counterflow re-measured in the same channel and under the same conditions. In both cases here is an initial fast decay which, for low enough initial line density approaches for a short time the form $t^{-1}$ characteristic of the decay of a random vortex tangle. This is followed at late times by a slower $t^{-3/2}$ decay, characteristic of the decay of large 'quasi-classical eddies'. However, in the range of investigated parameters, we observe always in the case of thermal counterflow, and only in a few cases of high steady-state velocity in superflow, an intermediate regime in which the decay either does not proceed monotonically with time or passes through a point of inflexion. This difference, established firmly by our experiments, might represent one essential ingredient for the full theoretical understanding of counterflow turbulence.
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New Heat-Capacity Measurements of the Possible Order-Disorder Transition in the 4/7-phase of 2D Helium: We have developed a new heat-capacity measuring system with ZYX graphite that is known to have much better crystallinity than Grafoil and started data collection. We report preliminary data as well as a detailed description of instrumentation including a mechanical heat-switch operated by hydraulic pressure of superfluid helium-4.
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Non-perturbative embedding of local defects in crystalline materials: We present a new variational model for computing the electronic first-order density matrix of a crystalline material in presence of a local defect. A natural way to obtain variational discretizations of this model is to expand the difference Q between the density matrix of the defective crystal and the density matrix of the perfect crystal, in a basis of precomputed maximally localized Wannier functions of the reference perfect crystal. This approach can be used within any semi-empirical or Density Functional Theory framework.
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Formation of a condensed state with macroscopic number of phonons in ultracold Bose gases: A mechanism for the formation of a new type of stationary state with macroscopical number of phonons in condensed atomic gases is proposed. This mechanism is based on generating longitudinal phonons as a result of parametric resonance caused by a permanent modulation of the transverse trap frequency in an elongated trap. The phonon-phonon interaction predetermines the self-consistent evolution which is completed with macroscopic population of one from all levels within the energy interval of parametric amplification. This level proves to be shifted to the edge of this interval. All other levels end the evolution with zero population.
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Exponentially Fragile PT-Symmetry in Lattices with Localized Eigenmodes: We study the effect of localized modes in lattices of size N with parity-time (PT) symmetry. Such modes are arranged in pairs of quasi-degenerate levels with splitting delta exp{-N/xi}, where \xi is their localization length. The level "evolution" with respect to the PT breaking parameter gamma shows a cascade of bifurcations during which a pair of real levels becomes complex. The spontaneous PT symmetry breaking occurs at gamma min(delta), thus resulting in an exponentially narrow exact PT phase. As N/xi decreases, it becomes more robust with gamma (1/N)^2 and the distribution P(gamma) changes from log-normal to semi-Gaussian. Our theory can be tested in the frame of optical lattices.
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Three-body Recombination of Lithium-6 Atoms with Large Negative Scattering Lengths: The 3-body recombination rate at threshold for distinguishable atoms with large negative pair scattering lengths is calculated in the zero-range approximation. The only parameters in this limit are the 3 scattering lengths and the Efimov parameter, which can be complex valued. We provide semi-analytic expressions for the cases of 2 or 3 equal scattering lengths and we obtain numerical results for the general case of 3 different scattering lengths. Our general result is applied to the three lowest hyperfine states of Lithium-6 atoms. Comparisons with recent experiments provide indications of loss features associated with Efimov trimers near the 3-atom threshold.
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Spin dynamics of a trapped spin-1 Bose Gas above the Bose-Einstein transition temperature: We study collective spin oscillations in a spin-1 Bose gas above the Bose-Einstein transition temperature. Starting from the Heisenberg equation of motion, we derive a kinetic equation describing the dynamics of a thermal gas with the spin-1 degree of freedom. Applying the moment method to the kinetic equation, we study spin-wave collective modes with dipole symmetry. The dipole modes in the spin-1 system are found to be classified into the three type of modes. The frequency and damping rate are obtained as functions of the peak density. The damping rate is characterized by three relaxation times associated with collisions.
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Lindemann Criterion and the Anomalous Melting Curve of Sodium: Recent reports of the melting curve of sodium at high pressure have shown that it has a very steep descent after a maximum of around 1000K at 31 GPa. This is not due to a phase transition. According to the Lindemann criterion, this behaviour should be apparent in the evolution of the Debye temperature with pressure. In this work, we have performed an "ab-initio" analysis of the behaviour of both the Debye temperature and the elastic constants up to 102 GPa, and find a clear trend at high pressure that should cause a noticeable effect on the melting curve.
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Parametric spin excitations in lateral quantum dots: In this work, the spin dynamics of a single electron under parametric modulation of a lateral quantum dot's electrostatic potential in the presence of spin-orbit coupling is investigated. Numerical and theoretical calculations demonstrate that, by squeezing and/or moving the electron's wave function, spin rotations with Rabi frequencies on the order of tens of megahertz can be achieved with experimentally accessible parameters in both parabolic and square lateral quantum dots. Applications of parametric excitations for determining spin-orbit coupling parameters and for increasing the spin polarization in the electronic ground are demonstrated.
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Exact Study of the 1D Boson Hubbard Model with a Superlattice Potential: We use Quantum Monte Carlo simulations and exact diagonalization to explore the phase diagram of the Bose-Hubbard model with an additional superlattice potential. We first analyze the properties of superfluid and insulating phases present in the hard-core limit where an exact analytic treatment is possible via the Jordan-Wigner transformation. The extension to finite on-site interaction is achieved by means of quantum Monte Carlo simulations. We determine insulator/superfluid phase diagrams as functions of the on-site repulsive interaction, superlattice potential strength, and filling, finding that insulators with fractional occupation numbers, which are present in the hard-core case, extend deep into the soft-core region. Furthermore, at integer fillings, we find that the competition between the on-site repulsion and the superlattice potential can produce a phase transition between a Mott insulator and a charge density wave insulator, with an intermediate superfluid phase. Our results are relevant to the behavior of ultracold atoms in optical superlattices which are beginning to be studied experimentally.
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Experimental study of the transport of coherent interacting matter-waves in a 1D random potential induced by laser speckle: We present a detailed analysis of the 1D expansion of a coherent interacting matterwave (a Bose-Einstein condensate) in the presence of disorder. A 1D random potential is created via laser speckle patterns. It is carefully calibrated and the self-averaging properties of our experimental system are discussed. We observe the suppression of the transport of the BEC in the random potential. We discuss the scenario of disorder-induced trapping taking into account the radial extension in our experimental 3D BEC and we compare our experimental results with the theoretical predictions.
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Topological quantum correction to an atomic ideal gas law as a dark energy effect: The traditional ambiguity about the bulk electrostatic potentials in crystals is due to the conditional convergence of Coulomb series. The classical Ewald approach turns out to be the first one resolving this task as consistent with a translational symmetry. The latter result appears to be directly associated with the thermodynamic limit in crystals. In this case the solution can also be obtained upon direct lattice summation, but after subtracting the mean Bethe potential. As shown, this effect is associated with special periodic boundary conditions at infinity so as to neutralize an arbitrary choice of the unit-cell charge distribution. However, the fact that any additional potential exerted by some charge distribution must in turn affect that charge distribution in equilibrium is not discussed in the case at hand so far. Here we show that in the simplest event of gaseous atomic hydrogen as an example, the self-consistent mean-field-potential correction results in an additional pressure contribution to an ideal gas law. As a result, the corresponding correction to the sound velocity arises. Moreover, if gas in question is not bounded by any fixed volume, then some acceleration within that medium is expected. Addressed to the Friedman hypersphere, our result may be interesting in connection with the accelerating Universe revealed experimentally and discussed intensively.
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Vortex Properties of a Resonant Superfluid: The properties of a vortex in a rotating superfluid Fermi gas are studied in the unitary limit. A phenomenological approach based on Ginzburg-Landau theory is developed for this purpose. The density profiles, including those of the normal fluid and superfluid, are obtained at various temperatures and rotation frequencies. The superfluid and normal fluid densities can be identified from the angular momentum density. The total free energy and angular momentum of the vortex are also obtained.
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Dynamics of rapidly rotating Bose-Einstein condensates in a harmonic plus quartic trap: A two-dimensional rapidly rotating Bose-Einstein condensate in a harmonic plus quartic trap is expected to have unusual vortex states that do not occur in a pure harmonic trap. At a critical rotation speed $\Omega_h$, a central hole appears in the condensate, and at some faster rotation speed $\Omega_g$, the system undergoes a transition to a giant vortex state with pure irrotational flow. Using a time-dependent variational analysis, we study the behavior of an annular condensate with a single concentric ring of vortices. The transition to a giant vortex state is investigated by comparing the energy of the two equilibrium states (the ring of vortices and the giant vortex) and also by studying the dynamical stability of small excitation modes of the ring of vortices.
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Exactly solvable model of electron in the Lame potential and singularities of the electron thermodynamic potential: One-gap and two-gap separable Lame potentials are studied in detail. For the one-dimensional case, we construct the dispersion relation graph E(k) and for the three-dimensional case we construct the Fermi surfaces in the first and second bands. The pictures illustrate a passage from the limit case of free electrons to the limit case of tight binding electrons. These results are used to describe the Lifshits electron phase transition of 2.5 kind and derive some exact expressions. We also examine the singularities of the second derivative of magnetic momentum in an external magnetic field. The parameter of the singularities depends on corresponding effective mass.
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Half-vortices in polariton condensates: It is shown that vortices in linearly polarized polariton condensates in planar semiconductor microcavities carry two winding numbers (k,m). These numbers can be either integer or half-integer simultaneously. Four half-integer vortices (1/2,1/2), (-1/2,-1/2), (1/2,-1/2), and (-1/2,1/2) are anisotropic, possess the smallest energy, and define the Kosterlitz-Thouless transition temperature. The condensate concentration remains finite within the core of half-vortex and the polarization becomes fully circular in the core center.
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Influence of an external magnetic field on the decoherence of a central spin coupled to an antiferromagnetic environment: Using the spin wave approximation, we study the decoherence dynamics of a central spin coupled to an antiferromagnetic environment under the application of an external global magnetic field. The external magnetic field affects the decoherence process through its effect on the antiferromagnetic environment. It is shown explicitly that the decoherence factor which displays a Gaussian decay with time depends on the strength of the external magnetic field and the crystal anisotropy field in the antiferromagnetic environment. When the values of the external magnetic field is increased to the critical field point at which the spin-flop transition (a first-order quantum phase transition) happens in the antiferromagnetic environment, the decoherence of the central spin reaches its highest point. This result is consistent with several recent quantum phase transition witness studies. The influences of the environmental temperature on the decoherence behavior of the central spin are also investigated.
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Vortex-line solitons in a periodically modulated Bose gas: We study the nonlinear excitations of a vortex-line in a Bose-Einstein condensate trapped in a one-dimensional optical lattice. We find that the classical Euler dynamics of the vortex results in a description of the vortex line in terms of a (discrete) one-dimensional Gross-Pitaevskii equation, which allows for both bright and gray soliton solutions. We discuss these solutions in detail and predict that it is possible to create vortex-line solitons with current experimental capabilities.
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Neutron Reflection from the Surface of Liquid 4He with and without a Layer of 3He: We report and discuss the first neutron reflection measurements from the free surface of normal and superfluid 4He and of liquid 3He-4He mixture. In case of liquid 4He the surface roughness is different above and below the lambda transition, being smoother in the superfluid state. For the superfluid, we also observe the formation of a surface layer ~200 A thick which has a subtly different neutron scattering cross-section. The results can be interpreted as an enhancement of Bose-Einstein condensate fraction close to the helium surface. We find that the addition of 3He isotopic impurities leads to the formation of Andreev levels at low temperatures.
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Spin Collective Modes of Two-Species Fermi Liquids: Helium-3 and Atomic Gases near the Feshbach Resonance: We present theoretical findings on the spin collective modes of a two-species Fermi liquid, prepared alternatively in a polarized equilibrium or a polarized non-equilibrium state. We explore the effects on these modes of a diverging s-wave scattering length, as occurs near a Feshbach resonance in a Fermionic atomic gas. We compare these atomic gas modes with those of the conventional Helium-3 system, and we find that they differ from the conventional systems, and that the gap and spin stiffness are tunable via the Feshbach resonance.
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Statistical Facts of Artificial Stock Market: The paper reports the construction of artificial stock market that emerges the similar statistical facts with real data in Indonesian stock market. We use the individual but dominant data, i.e.: PT TELKOM in hourly interval. The artificial stock market shows standard statistical facts, e.g.: volatility clustering, the excess kurtosis of the distribution of return, and the scaling properties with its breakdown in the crossover of Levy distribution to the Gaussian one. From this point, the artificial stock market will always be evaluated in order to have comprehension about market process in Indonesian stock market generally.
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The role of the coherence in the cross-correlation analysis of diffraction patterns from two-dimensional dense mono-disperse systems: The investigation of the static and dynamic structural properties of colloidal systems relies on techniques capable of atomic resolution in real space and femtosecond resolution in time. Recently, the cross-correlation function (CCF) analysis of both X-rays and electron diffraction patterns from dilute and dense aggregates has demonstrated the ability to retrieve information on the sample's local order and symmetry. Open questions remain regarding the role of the beam coherence in the formation of the diffraction pattern and the properties of the CCF, especially in dense systems. Here, we simulate the diffraction patterns of dense two-dimensional monodisperse systems of different symmetries, varying the transverse coherence of the probing wave, and analyze their CCF. We study samples with different symmetries at different size scale, as for example, pentamers arranged into a four-fold lattice where each pentamer is surrounded by triangular lattices, both ordered and disordered. In such systems, different symmetry modulations are arising in the CCF at specific scattering vectors. We demonstrate that the amplitude of the CCF is a fingerprint of the degree of the ordering in the sample and that at partial transverse coherence, the CCF of a dense sample corresponds to that of an individual scattering object.
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Quantized vortices in atomic Bose-Einstein condensates: In this review, we give an overview of the experimental and theoretical advances in the physics of quantized vortices in dilute atomic-gas Bose--Einstein condensates in a trapping potential, especially focusing on experimental research activities and their theoretical interpretations. Making good use of the atom optical technique, the experiments have revealed many novel structural and dynamic properties of quantized vortices by directly visualizing vortex cores from an image of the density profiles. These results lead to a deep understanding of superfluid hydrodynamics of such systems. Typically, vortices are stabilized by a rotating potential created by a laser beam, magnetic field, and thermal gas. Finite size effects and inhomogeneity of the system, originating from the confinement by the trapping potential, yield unique vortex dynamics coupled with the collective excitations of the condensate. Measuring the frequencies of the collective modes is an accurate tool for clarifying the character of the vortex state. The topics included in this review are the mechanism of vortex formation, equilibrium properties, and dynamics of a single vortex and those of a vortex lattice in a rapidly rotating condensate.
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Simulations of financial markets in a Potts-like model: A three-state model based on the Potts model is proposed to simulate financial markets. The three states are assigned to "buy", "sell" and "inactive" states. The model shows the main stylized facts observed in the financial market: fat-tailed distributions of returns and long time correlations in the absolute returns. At low inactivity rate, the model effectively reduces to the two-state model of Bornholdt and shows similar results to the Bornholdt model. As the inactivity increases, we observe the exponential distributions of returns.
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Low-Temperature Mobility of Surface Electrons and Ripplon-Phonon Interaction in Liquid Helium: The low-temperature dc mobility of the two-dimensional electron system localized above the surface of superfluid helium is determined by the slowest stage of the longitudinal momentum transfer to the bulk liquid, namely, by the interaction of surface and volume excitations of liquid helium, which rapidly decreases with temperature. Thus, the temperature dependence of the low-frequency mobility is \mu_{dc} = 8.4x10^{-11}n_e T^{-20/3} cm^4 K^{20/3}/(V s), where n_e is the surface electron density. The relation T^{20/3}E_\perp^{-3} << 2x10^{-7} between the pressing electric field (in kV/cm) and temperature (in K) and the value \omega < 10^8 T^5 K^{-5}s^{-1} of the driving-field frequency have been obtained, at which the above effect can be observed. In particular, E_\perp = 1 kV/cm corresponds to T < 70 mK and \omega/2\pi < 30 Hz.
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Binding Energies of 6Li p-wave Feshbach Molecules: We present measurements of the binding energies of $^6$Li p-wave Feshbach molecules formed in combinations of the (F = 1/2, m_F = +1/2), (1), and (F = 1/2, m_F = -1/2), (2), states. The binding energies scale linearly with magnetic field detuning for all three resonances. The relative molecular magnetic moments are found to be $113 \pm 7 \mu$K/G, $111 \pm 6 \mu$K/G and $118 \pm 8 \mu$K/G for the (1)-(1), (1)-(2) and (2)-(2) resonances, respectively, in good agreement with theoretical predictions. Closed channel amplitudes and the size of the p-wave molecules are obtained theoretically from full closed-coupled calculations.
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Rotating states for trapped bosons in an optical lattice: Rotational states for trapped bosons in an optical lattice are studied in the framework of the Hubbard model. Critical frequencies are calculated and the main parameter regimes are identified. Transitions are observed from edge superfluids to vortex lattices with Mott insulating cores, and subsequently to lattices of interstitial vortices. The former transition coincides with the Mott transition. Changes in symmetry of the vortex lattices are observed as a function of lattice depth. Predictions for experimental signatures are presented.
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Two objective and independent fracture parameters for interface cracks and a paradox: Due to the oscillatory singular stress field around a crack tip, interface fracture has some peculiar features. This paper is focused on two of them. One can be reflected by a proposed paradox that geometrically similar structures with interface cracks under similar loadings may have different failure behaviors. The other one is that the existing fracture parameters of the oscillatory singular stress field, such as a complex stress intensity factor, exhibit some non-objectivity because their phase angle depend on an arbitrarily chosen length. Two objective and independent fracture parameters are proposed which can fully characterize the stress field near the crack tip. One parameter represents the stress intensity with classical unit of stress intensity factors. It is interesting to find that the loading mode can be characterized by a length as the other parameter, which can properly reflect the phase of the stress oscillation with respect to the distance to the crack tip. This is quite different from other crack tip fields in which the loading mode is usually expressed by a phase angle. The corresponding failure criterion for interface cracks does not include any arbitrarily chosen quantity, and therefore is convenient for comparing and accumulating experimental results, even existing ones.
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Condon domains - these non-magnetic diamagnetic domains: The paper, not pretending for a complete and detailed review, is intended mainly for a wide community of physicists, not only specialists in this particular subject. The author gives a physical picture of the periodic emergence of instabilities and well-known diamagnetic domains (Condon domains) in metals resulting from the strong de Haas-van Alphen effect. The most significant experiments on observation and study of the domain state in metals are described. In particular, the recent achievements in this area using muon spin rotation, as well as the amazing phenomenon of "supersoftness" observed in the magnetostriction experiments, are presented. Novel, not previously discussed features of the phenomenon related to the metal compressibility are enlightened.
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La-dilution effects in TbRhIn5 antiferromagnet: We report measurements of temperature dependent magnetic susceptibility, resonant x-ray magnetic scattering (XRMS) and heat capacity on single crystals of Tb1-xLaxRhIn5 for nominal concentrations in the range 0.0 < x < 1.0. TbRhIn5 is an antiferromagnetic (AFM) compound with TN ~ 46 K, which is the highest TN values along the RRhIn5 series. We explore the suppression of the antiferromagnetic (AFM) state as a function of La-doping considering the effects of La-induced dilution and perturbations to the tetragonal crystalline electrical field (CEF) on the long range magnetic interaction between the Tb$^{3+}$ ions. Additionally, we also discuss the role of disorder. Our results and analysis are compared to the properties of the undoped compound and of other members of the RRhIn5 family and structurally related compounds (R2RhIn8 and RIn3). The XRMS measurements reveal that the commensurate magnetic structure with the magnetic wave-vector (0,1/2,1/2) observed for the undoped compound is robust against doping perturbations in Tb0.6La0.4RhIn5 compound.
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Magnetism and structure of magnetic multilayers based on the fully spin polarized Heusler alloys Co2MnGe and Co2MnSn: Our Introduction starts with a short general review of the magnetic and structural properties of the Heusler compounds which are under discussion in this book. Then, more specifically, we come to the discussion of our experimental results on multilayers composed of the Heusler alloys Co2MnGe and Co2MnSn with V or Au as interlayers. The experimental methods we apply combine magnetization and magneto-resistivity measurements, x-ray diffraction and reflectivity, soft x-ray magnetic circular dichroism and spin polarized neutron reflectivity. We find that below a critical thickness of the Heusler layers at typically dcr = 1.5 nm the ferromagnetic order is lost and spin glass order occurs instead. For very thin ferromagnetic Heusler layers there are peculiarities in the magnetic order which are unusual when compared to conventional ferromagnetic transition metal multilayer systems. In [Co2MnGe/Au] multilayers there is an exchange bias shift at the ferromagnetic hysteresis loops at low temperatures caused by spin glass ordering at the interface. In [Co2MnGe/V] multilayers we observe an antiferromagnetic interlayer long range ordering below a well defined Neel temperature originating from the dipolar stray fields at the magnetically rough Heusler layer interfaces.
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Anomalous reflection and excitation of surface waves in metamaterials: We consider reflection of electromagnetic waves from layered structures with various dielectric and magnetic properties, including metamaterials. Assuming periodic variations in the permittivity, we find that the reflection is in general anomalous. In particular, we note that the specular reflection vanishes and that the incident energy is totally reflected in the backward direction, when the conditions for resonant excitation of leaking surface waves are fulfilled.
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