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3.0

Jun 30, 2018
06/18

by
Nicolas Cherroret; Benoît Vermersch; Jean Claude Garreau; Dominique Delande

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In disordered systems, our present understanding of the Anderson transition is hampered by the possible presence of interactions between particles. We demonstrate that in boson gases, even weak interactions deeply alter the very nature of the Anderson transition. While there still exists a critical point in the system, below that point a novel phase appears, displaying a new critical exponent, subdiffusive transport and a breakdown of the one-parameter scaling description of Anderson...

Topics: Disordered Systems and Neural Networks, Condensed Matter

Source: http://arxiv.org/abs/1401.1038

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6.0

Jun 30, 2018
06/18

by
Alexei Andreanov; Andrei A. Fedorenko

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We study the dynamics of excitations in a system of $O(N)$ quantum rotors in the presence of random fields and random anisotropies. Below the lower critical dimension $d_{\mathrm{lc}}=4$ the system exhibits a quasi-long-range order with a power-law decay of correlations. At zero temperature the spin waves are localized at the length scale $L_{\mathrm{loc}}$ beyond which the quantum tunneling is exponentially suppressed $ c \sim e^{-(L/L_{\mathrm{loc}})^{2(\theta+1)}}$. At finite temperature $T$...

Topics: Disordered Systems and Neural Networks, Condensed Matter

Source: http://arxiv.org/abs/1403.5529

3
3.0

Jun 30, 2018
06/18

by
Peter Sollich; Daniele Tantari; Alessia Annibale; Adriano Barra

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We use belief-propagation techniques to study the equilibrium behavior of a bipartite spin-glass, with interactions between two sets of $N$ and $P = \alpha N$ spins. Each spin has a finite degree, i.e.\ number of interaction partners in the opposite set; an equivalent view is then of a system of $N$ neurons storing $P$ diluted patterns. We show that in a large part of the parameter space of noise, dilution and storage load, delimited by a critical surface, the network behaves as an extensive...

Topics: Disordered Systems and Neural Networks, Condensed Matter

Source: http://arxiv.org/abs/1404.3654

3
3.0

Jun 30, 2018
06/18

by
Xiaojun Cheng; Yitzchak Lockerman; Azriel Z. Genack

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We follow the trajectories of phase singularities at nulls of intensity in the speckle pattern of waves transmitted through random media as the frequency of the incident radiation is scanned in microwave experiments and numerical simulations. Phase singularities are observed to diffuse with a linear increase of the square displacement with frequency shift. The product of the diffusion coefficient of phase singularities in the transmitted speckle pattern and the photon diffusion coefficient...

Topics: Disordered Systems and Neural Networks, Condensed Matter

Source: http://arxiv.org/abs/1405.4818

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5.0

Jun 30, 2018
06/18

by
D. L. Stein

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As Phil Anderson noted long ago, frustration can be generally defined by measuring the fluctuations in the coupling energy across a plane boundary between two large blocks of material. Since that time, a number of groups have studied the free energy fluctuations between (putative) distinct spin glass thermodynamic states. While upper bounds on such fluctuations have been obtained, useful lower bounds have been more difficult to derive. I present a history of these efforts, and briefly discuss...

Topics: Disordered Systems and Neural Networks, Condensed Matter

Source: http://arxiv.org/abs/1406.0816

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3.0

Jun 30, 2018
06/18

by
H. Terletska; C. E. Ekuma; C. Moore; K. -M. Tam; J. Moreno; M. Jarrell

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We generalize the typical medium dynamical cluster approximation (TMDCA) and the local Blackman, Esterling, and Berk (BEB) method for systems with off-diagonal disorder. Using our extended formalism we perform a systematic study of the effects of non-local disorder-induced correlations and of off-diagonal disorder on the density of states and the mobility edge of the Anderson localized states. We apply our method to the three-dimensional Anderson model with configuration dependent hopping and...

Topics: Disordered Systems and Neural Networks, Condensed Matter

Source: http://arxiv.org/abs/1406.1235

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10.0

Jun 27, 2018
06/18

by
Atanu Nandy; Arunava Chakrabarti

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Exact construction of one electron eigenstates with flat, non-dispersive bands, and localized over clusters of various sizes is reported for a class of quasi-one dimensional looped networks. Quasiperiodic Fibonacci and Berker fractal geometries are embedded in the arms of the loop threaded by a uniform magnetic flux. We work out an analytical scheme to unravel the localized single particle states pinned at various atomic sites or over clusters of them. The magnetic field is varied to control,...

Topics: Disordered Systems and Neural Networks, Condensed Matter

Source: http://arxiv.org/abs/1506.00386

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6.0

Jun 29, 2018
06/18

by
Alejandro Seif; Tomas S. Grigera

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We revisit the $t154$ variant of the Biroli-Mezard lattice glass, complementing previous studies by studying statics and dynamics under periodic boundary conditions as well as systems confined in cavities with amorphous boundaries. We compute the point-to-se correlation and relaxation times under the different boundary conditions. Results point to a scenario with dynamics ruled by structural correlations.

Topics: Disordered Systems and Neural Networks, Condensed Matter

Source: http://arxiv.org/abs/1611.06754

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5.0

Jun 29, 2018
06/18

by
Nikolaos G. Fytas; Victor Martin-Mayor; Marco Picco; Nicolas Sourlas

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The random-field Ising model is one of the few disordered systems where the perturbative renormalization group can be carried out to all orders of perturbation theory. This analysis predicts dimensional reduction, i.e., that the critical properties of the random-field Ising model in $D$ dimensions are identical to those of the pure Ising ferromagnet in $D-2$ dimensions. It is well known that dimensional reduction is not true in three dimensions, thus invalidating the perturbative...

Topics: Disordered Systems and Neural Networks, Condensed Matter

Source: http://arxiv.org/abs/1612.06156

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5.0

Jun 29, 2018
06/18

by
Cecile Monthus

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The finite temperature dynamics of the Dyson hierarchical classical spins models is studied via real-space renormalization rules concerning the couplings and the relaxation times. For the ferromagnetic model involving Long-Ranged coupling $J(r) \propto r^{-1-\sigma}$ in the region $1/2

Topics: Disordered Systems and Neural Networks, Condensed Matter

Source: http://arxiv.org/abs/1601.05643

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6.0

Jun 30, 2018
06/18

by
Silvia Bartolucci; Alessia Annibale

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In this work we solve the dynamics of pattern diluted associative networks, evolving via sequential Glauber update. We derive dynamical equations for the order parameters, that quantify the simultaneous pattern recall of the system, and analyse the nature and stability of the stationary solutions by means of linear stability analysis as well as Monte Carlo simulations. We investigate the parallel retrieval capabilities of the system in different regions of the phase space, in particular in the...

Topics: Disordered Systems and Neural Networks, Condensed Matter

Source: http://arxiv.org/abs/1405.2454

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Jun 30, 2018
06/18

by
Yichen Huang; Joel E. Moore

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We study the representational power of a Boltzmann machine (a type of neural network) in quantum many-body systems. We prove that any (local) tensor network state has a (local) neural network representation. The construction is almost optimal in the sense that the number of parameters in the neural network representation is almost linear in the number of nonzero parameters in the tensor network representation. Despite the difficulty of representing (gapped) chiral topological states with local...

Topics: Disordered Systems and Neural Networks, Condensed Matter

Source: http://arxiv.org/abs/1701.06246

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6.0

Jun 30, 2018
06/18

by
M Carrillo; J A González; S Hernández; C López; A Raya

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Within an artificial neural network (ANN) approach, we classify simulated signals corresponding to the semi-classical description of Bloch oscillations on a two-dimensional square lattice. After the ANN is properly trained, we consider the inverse problem of Bloch oscillations (BO) in which a new signal is classified according to the lattice spacing and external electric field strength oriented along a particular direction of the lattice with an accuracy of 96%. This approach can be improved...

Topics: Disordered Systems and Neural Networks, Condensed Matter

Source: http://arxiv.org/abs/1704.08346

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Jun 26, 2018
06/18

by
V. Janis; A. Kauch; A. Klic

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We discuss ergodicity breaking in frustrated disordered systems with no apparent broken symmetry of the Hamiltonian and present a way how to amend it in the low-temperature phase. We demonstrate this phenomenon on mean-field models of spin glasses. We use replicas of the spin variables to test thermodynamic homogeneity of ergodic equilibrium systems. We show that replica-symmetry breaking reflects ergodicity breaking and is used to restore an ergodic state. We then present explicit asymptotic...

Topics: Condensed Matter, Disordered Systems and Neural Networks

Source: http://arxiv.org/abs/1501.01653

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7.0

Jun 28, 2018
06/18

by
D. B. Gutman; I. V. Protopopov; A. L. Burin; I. V. Gornyi; R. A. Santos; A. D. Mirlin

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We study the heat conductivity in Anderson insulators in the presence of power-law interaction. Particle-hole excitations built on localized electron states are viewed as two-level systems randomly distributed in space and energy and coupled due to electron-electron interaction. A small fraction of these states form resonant pairs that in turn build a complex network allowing for energy propagation. We identify the character of energy transport through this network and evaluate the thermal...

Topics: Disordered Systems and Neural Networks, Condensed Matter

Source: http://arxiv.org/abs/1512.06705

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5.0

Jun 28, 2018
06/18

by
Hisamitsu Mukaida

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The effective potential for the two-replica system of the random energy model is exactly derived. It is an analytic function of the magnetizations of two replicas, $\varphi^1$ and $\varphi^2$ in the high-temperature phase. In the low-temperature phase, where the replica symmetry breaking takes place, the effective potential becomes non-analytic when $\varphi^1=\varphi^2$. The non-analyticity is considered as a consequence of the condensation of the Boltzmann measure, which is a typical property...

Topics: Disordered Systems and Neural Networks, Condensed Matter

Source: http://arxiv.org/abs/1510.02613

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Jun 26, 2018
06/18

by
Laszlo Ujfalusi; Imre Varga

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The disorder induced metal--insulator transition is investigated in a three-dimensional simple cubic lattice and compared for the presence and absence of time-reversal and spin-rotational symmetry, i.e. in the three conventional symmetry classes. Large scale numerical simulations have been performed on systems with linear sizes up to $L=100$ in order to obtain eigenstates at the band center, $E=0$. The multifractal dimensions, exponents $D_q$ and $\alpha_q$, have been determined in the range of...

Topics: Condensed Matter, Disordered Systems and Neural Networks

Source: http://arxiv.org/abs/1501.02147

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10.0

Jun 26, 2018
06/18

by
C. C. Alan Fung; S. -I. Amari

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Attractor models are simplified models used to describe the dynamics of firing rate profiles of a pool of neurons. The firing rate profile, or the neuronal activity, is thought to carry information. Continuous attractor neural networks (CANNs) describe the neural processing of continuous information such as object position, object orientation and direction of object motion. Recently, it was found that, in one-dimensional CANNs, short-term synaptic depression can destabilize bump-shaped neuronal...

Topics: Disordered Systems and Neural Networks, Condensed Matter

Source: http://arxiv.org/abs/1502.00127

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6.0

Jun 30, 2018
06/18

by
Carlo Lucibello; Flaviano Morone; Giorgio Parisi; Federico Ricci-Tersenghi; Tommaso Rizzo

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We derive the analytical expression for the first finite size correction to the average free energy of disordered Ising models on random regular graphs. The formula can be physically interpreted as a weighted sum over all non self-intersecting loops in the graph, the weight being the free-energy shift due to the addition of the loop to an infinite tree.

Topics: Disordered Systems and Neural Networks, Condensed Matter

Source: http://arxiv.org/abs/1403.6049

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5.0

Jun 28, 2018
06/18

by
M. Yépez; J. J. Sáenz

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The statistical scattering properties of wave transport in disordered waveguides are derived perturbatively within the transition matrix formalism. The limiting macroscopic statistic of the wave transport, emerges as a consequence of a generalized central-limit-theorem: the expectation values of macroscopic observables depend only on the first and second moments of the reflection matrix of individual scatterers. This theoretical approach does not consider any statistical assumption on the...

Topics: Disordered Systems and Neural Networks, Condensed Matter

Source: http://arxiv.org/abs/1511.07931

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7.0

Jun 29, 2018
06/18

by
Stefan Kettemann

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We consider the orthogonality catastrophe at the Anderson Metal-Insulator transition (AMIT). The typical overlap $F$ between the ground state of a Fermi liquid and the one of the same system with an added potential impurity is found to decay at the AMIT exponentially with system size $L$ as $F \sim \exp (- \langle I_A\rangle /2)= \exp(-c L^{\eta})$, where $I_A$ is the so called Anderson integral, $\eta $ is the power of multifractal intensity correlations and $\langle ... \rangle$ denotes the...

Topics: Disordered Systems and Neural Networks, Condensed Matter

Source: http://arxiv.org/abs/1606.02243

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8.0

Jun 30, 2018
06/18

by
M. Pino; V. E. Kravtsov; B. L. Altshuler; L. B. Ioffe

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We report the results of the numerical study of the non-dissipative quantum Josephson junction chain at high temperatures. The disorder in this chain is due to the random offset charges. This chain is one of the simplest physical systems to study many body localization. We show that at high temperatures the systems exhibits three distinct regimes: insulating, characterized by the full localization of many body wave function, fully delocalized (metallic) one characterized by the wave function...

Topics: Disordered Systems and Neural Networks, Condensed Matter

Source: http://arxiv.org/abs/1704.07393

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7.0

Jun 29, 2018
06/18

by
Danilo B. Liarte; O. Stenull; Xiaoming Mao; T. C. Lubensky

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We use numerical simulations and an effective-medium theory to study the rigidity percolation transition of the honeycomb and diamond lattices when weak bond-bending forces are included. We use a rotationally invariant bond-bending potential, which, in contrast to the Keating potential, does not involve any stretching. As a result, the bulk modulus does not depend on the bending stiffness $\kappa$. We obtain scaling functions for the behavior of some elastic moduli in the limits of small...

Topics: Disordered Systems and Neural Networks, Condensed Matter

Source: http://arxiv.org/abs/1601.06127

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5.0

Jun 29, 2018
06/18

by
K. S. Tikhonov; A. D. Mirlin; M. A. Skvortsov

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A numerical study of Anderson transition on random regular graphs (RRG) with diagonal disorder is performed. The problem can be described as a tight-binding model on a lattice with N sites that is locally a tree with constant connectivity. In certain sense, the RRG ensemble can be seen as infinite-dimensional ($d\to\infty$) cousin of Anderson model in d dimensions. We focus on the delocalized side of the transition and stress the importance of finite-size effects. We show that the data can be...

Topics: Disordered Systems and Neural Networks, Condensed Matter

Source: http://arxiv.org/abs/1604.05353

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4.0

Jun 29, 2018
06/18

by
Takayuki Narumi; Michio Tokuyama

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The kinetic glass transition in short-range attractive colloids is theoretically studied by time-convolutionless mode-coupling theory (TMCT). By numerical calculations, TMCT is shown to recover all the remarkable features predicted by the mode-coupling theory for attractive colloids, namely the glass-liquid-glass reentrant, the glass-glass transition, and the higher-order singularities. It is also demonstrated through the comparisons with the results of molecular dynamics for the binary...

Topics: Disordered Systems and Neural Networks, Condensed Matter

Source: http://arxiv.org/abs/1605.06594

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Jun 28, 2018
06/18

by
Y. M. Beltukov; C. Fusco; A. Tanguy; D. A. Parshin

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We show that harmonic vibrations in amorphous silicon can be decomposed to transverse and longitudinal components in all frequency range even in the absence of the well defined wave vector ${\bf q}$. For this purpose we define the transverse component of the eigenvector with given $\omega$ as a component, which does not change the volumes of Voronoi cells around atoms. The longitudinal component is the remaining orthogonal component. We have found the longitudinal and transverse components of...

Topics: Disordered Systems and Neural Networks, Condensed Matter

Source: http://arxiv.org/abs/1508.04252

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3.0

Jun 29, 2018
06/18

by
Barbara Bravi; Manfred Opper; Peter Sollich

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We present average performance results for dynamical inference problems in large networks, where a set of nodes is hidden while the time trajectories of the others are observed. Examples of this scenario can occur in signal transduction and gene regulation networks. We focus on the linear stochastic dynamics of continuous variables interacting via random Gaussian couplings of generic symmetry. We analyze the inference error, given by the variance of the posterior distribution over hidden paths,...

Topics: Disordered Systems and Neural Networks, Condensed Matter

Source: http://arxiv.org/abs/1607.01622

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5.0

Jun 29, 2018
06/18

by
T. Micklitz

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We investigate spectral correlations in quasi one-dimensional Anderson insulators with broken time-reversal symmetry. While energy levels are uncorrelated in the thermodynamic limit of infinite wire-length, some correlations remain in finite-size Anderson insulators. Asymptotic behaviors of level-level correlations in these systems are known in the large- and small-frequency limits, corresponding to the regime of classical diffusive dynamics and the deep quantum regime of strong Anderson...

Topics: Disordered Systems and Neural Networks, Condensed Matter

Source: http://arxiv.org/abs/1611.07271

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4.0

Jun 29, 2018
06/18

by
D. Mouhanna; G. Tarjus

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We revisit the thermodynamic behavior of the random-anisotropy O($N$) model by investigating its large-$N$ limit. We focus on the system at zero temperature where the mean-field-like artifacts of the large-$N$ limit are less severe. We analyze the connection between the description in terms of self-consistent Schwinger-Dyson equations and the functional renormalization group. We provide a unified description of the phase diagram and critical behavior of the model and clarify the nature of the...

Topics: Disordered Systems and Neural Networks, Condensed Matter

Source: http://arxiv.org/abs/1607.08515

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3.0

Jun 29, 2018
06/18

by
O. S. Vershinina; E. A. Kozinov; T. V. Laptyeva; S. V. Denisov; M. V. Ivanchenko

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Disorder in a 1D quantum lattice induces Anderson localization of the eigenstates and drastically alters transport properties of the lattice. In the original Anderson model, the addition of a periodic driving increases, in a certain range of the driving's frequency and amplitude, localization length of the appearing Floquet eigenstates. We go beyond the uncorrelated disorder case and address the experimentally relevant situation when spatial correlations are present in the lattice potential....

Topics: Disordered Systems and Neural Networks, Condensed Matter

Source: http://arxiv.org/abs/1610.08682

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3.0

Jun 29, 2018
06/18

by
Scott D. Geraedts; R. N. Bhatt

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The dynamics of the highly excited states of a system projected into a single Landau level are analyzed. An analysis of level spacing ratios for finite size systems shows a clear crossover from extend (GUE) to localized (Poisson) statistics, indicating a many body localization transition. However, the location of this transition depends very strongly on system size, and appears to scale to infinite disorder in the thermodynamic limit. This result does not depend on the properties of the ground...

Topics: Disordered Systems and Neural Networks, Condensed Matter

Source: http://arxiv.org/abs/1610.08931

3
3.0

Jun 30, 2018
06/18

by
Joshua D. Bodyfelt; Daniel Leykam; Carlo Danieli; Xiaoquan Yu; Sergej Flach

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Flat band networks are characterized by coexistence of dispersive and flat bands. Flat bands (FB) are generated by compact localized eigenstates (CLS) with local network symmetries, based on destructive interference. Correlated disorder and quasiperiodic potentials hybridize CLS without additional renormalization, yet with surprising consequencies: (i) states are expelled from the FB energy $E_{FB}$, (ii) the localization length of eigenstates vanishes as $\xi \sim 1 / \ln (E- E_{FB})$, (iii)...

Topics: Disordered Systems and Neural Networks, Condensed Matter

Source: http://arxiv.org/abs/1407.8345

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6.0

Jun 30, 2018
06/18

by
Andreas Heuer; Lars Luehning

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Nonlinear effects are omnipresent in thin films of ion conducting materials showing up as a significant increase of the conductivity. For a disordered hopping model general physical mechanisms are identified giving rise to the occurrence of positive or negative nonlinear effects, respectively. Analytical results are obtained in the limit of high but finite dimensions. They are compared with the numerical results for 3D up to 6D systems. A very good agreement can be found, in particular for...

Topics: Disordered Systems and Neural Networks, Condensed Matter

Source: http://arxiv.org/abs/1402.3615

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5.0

Jun 30, 2018
06/18

by
V. P. Michal; B. L. Altshuler; G. V. Shlyapnikov

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We consider weakly interacting bosons in a 1D quasiperiodic potential (Aubry-Azbel-Harper model) in the regime where all single-particle states are localized. We show that the interparticle interaction may lead to the many-body delocalization and we obtain the finite-temperature phase diagram. Counterintuitively, in a wide range of parameters the delocalization requires stronger cou- pling as the temperature increases. This means that the system of bosons can undergo a transition from a fluid...

Topics: Disordered Systems and Neural Networks, Condensed Matter

Source: http://arxiv.org/abs/1402.4796

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6.0

Jun 30, 2018
06/18

by
Leonardo Ermann; Dima L. Shepelyansky

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We study numerically the frequency modulated kicked nonlinear rotator with effective dimension $d=1,2,3,4$. We follow the time evolution of the model up to $10^9$ kicks and determine the exponent $\alpha$ of subdiffusive spreading which changes from $0.35$ to $0.5$ when the dimension changes from $d=1$ to $4$. All results are obtained in a regime of relatively strong Anderson localization well below the Anderson transition point existing for $d=3,4$. We explain that this variation of the...

Topics: Disordered Systems and Neural Networks, Condensed Matter

Source: http://arxiv.org/abs/1403.2692

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3.0

Jun 30, 2018
06/18

by
Elena Agliari; Adriano Barra; Andrea Galluzzi; Francesco Guerra; Daniele Tantari; Flavia Tavani

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In this work we study a Hebbian neural network, where neurons are arranged according to a hierarchical architecture such that their couplings scale with their reciprocal distance. As a full statistical mechanics solution is not yet available, after a streamlined introduction to the state of the art via that route, the problem is consistently approached through signal- to-noise technique and extensive numerical simulations. Focusing on the low-storage regime, where the amount of stored patterns...

Topics: Disordered Systems and Neural Networks, Condensed Matter

Source: http://arxiv.org/abs/1409.0227

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Jun 25, 2018
06/18

by
Alessia Annibale; Anthony C. C. Coolen; Nuria Planell-Morell

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Protein interaction networks (PIN) are popular means to visualize the proteome. However, PIN datasets are known to be noisy, incomplete and biased by the experimental protocols used to detect protein interactions. This paper aims at understanding the connection between true protein interactions and the protein interaction datasets that have been obtained using the most popular experimental techniques, i.e. mass spectronomy (MS) and yeast two-hybrid (Y2H). We show that the most natural adjacency...

Topics: Disordered Systems and Neural Networks, Condensed Matter

Source: http://arxiv.org/abs/1501.00662

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Jun 29, 2018
06/18

by
Alexander Altland; Tobias Micklitz

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We construct an analytic theory of many-body localization (MBL) in random spin chains. The approach is based on a first quantized perspective in which MBL is understood as a localization phenomenon on the high dimensional lattice defined by the discrete Hilbert space of the clean system. We construct a field theory on that lattice and apply it to discuss the stability of a weak disorder (`Wigner-Dyson') and a strong disorder (`Poisson') phase.

Topics: Disordered Systems and Neural Networks, Condensed Matter

Source: http://arxiv.org/abs/1609.00877

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3.0

Jun 30, 2018
06/18

by
S. V. Isakov; I. N. Zintchenko; T. F. Rønnow; M. Troyer

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We present several efficient implementations of the simulated annealing algorithm for Ising spin glasses on sparse graphs. In particular, we provide a generic code for any choice of couplings, an optimized code for bipartite graphs, and highly optimized implementations using multi-spin coding for graphs with small maximum degree and discrete couplings with a finite range. The latter codes achieve up to 50 spin flips per nanosecond on modern Intel CPUs. We also compare the performance of the...

Topics: Disordered Systems and Neural Networks, Condensed Matter

Source: http://arxiv.org/abs/1401.1084

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Jun 27, 2018
06/18

by
Huanan Li; Andrea Kleeman; Tsampikos Kottos; Boris Shapiro

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We investigate sound propagation in a moving fluid confined in a randomly corrugated tube. For weak randomness and small fluid velocities $v^{(0)}$, the localization length $\xi$ shows extreme sensitivity to the variation of $v^{(0)}$. In the opposite limit of large fluid velocities, $\xi$ acquires a constant value which is independent of the frequency of the incident sound wave, the degree of randomness and $v^{(0)}$ itself. Finally, we find that the standard deviation $\sigma_{\ln T}$ of the...

Topics: Disordered Systems and Neural Networks, Condensed Matter

Source: http://arxiv.org/abs/1506.01114

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Jun 28, 2018
06/18

by
Juntao Song; Emil Prodan

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In the strictly periodic setting, the electric polarization of inversion-symmetric solids with and without time-reversal symmetry and the isotropic magneto-electric response function of time-reversal symmetric insulators are known to be topological invariants displaying an exact $\mathbb Z_2$ quantization. This quantization is stabilized by the symmetries. In the present work, we investigate the fate of such symmetry-stabilized topological invariants in the presence of a disorder which breaks...

Topics: Disordered Systems and Neural Networks, Condensed Matter

Source: http://arxiv.org/abs/1507.02605

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Jun 28, 2018
06/18

by
Canran Xu; Maxim G. Vavilov

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We consider a one dimensional spin $1/2$ chain with Heisenberg interaction in a disordered parallel magnetic field. This system is known to exhibit the many body localization (MBL) transition at critical strength of disorder. We analyze the response of the chain when additional perpendicular magnetic field is applied to an individual spin and propose a method for accurate determination of the mobility edge via local spin measurements. We further demonstrate that the exponential decrease of the...

Topics: Disordered Systems and Neural Networks, Condensed Matter

Source: http://arxiv.org/abs/1509.05158

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3.0

Jun 28, 2018
06/18

by
T. Bryk; I. Mryglod

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We comment on three incorrect claims in the paper by Fomin et al (arXiv:1507.06094) concerning the generalized hydrodynamic methodology and positive sound dispersion in fluids.

Topics: Disordered Systems and Neural Networks, Condensed Matter

Source: http://arxiv.org/abs/1510.07093

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5.0

Jun 30, 2018
06/18

by
M. C. Diamantini; C. A. Trugenberger

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The classic Landauer bound can be lowered when erasure errors are permitted. Here we point out that continuous phase transitions characterized by an order parameter can also be viewed as information erasure by resetting a certain number of bits to a standard value. The information-theoretic expression for the generalized Landauer bound in terms of error probability implies thus a universal form for the thermodynamic entropy in the partially ordered phase. We explicitly show that the...

Topics: Disordered Systems and Neural Networks, Condensed Matter

Source: http://arxiv.org/abs/1403.5416

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Jun 27, 2018
06/18

by
Douglas N. Arnold; Guy David; David Jerison; Svitlana Mayboroda; Marcel Filoche

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The amplitude of localized quantum states in random or disordered media may exhibit long range exponential decay. We present here a theory that unveils the existence of an effective potential which finely governs the confinement of these states. In this picture, the boundaries of the localization subregions for low energy eigenfunctions correspond to the barriers of this effective potential, and the long range exponential decay characteristic of Anderson localization is explained as the...

Topics: Disordered Systems and Neural Networks, Condensed Matter

Source: http://arxiv.org/abs/1505.02684

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Jun 27, 2018
06/18

by
C. E. Ekuma; C. Moore; H. Terletska; K. -M. Tam; N. S. Vidhyadhiraja; J. Moreno; M. Jarrell

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We use the recently developed typical medium dynamical cluster (TMDCA) approach~[Ekuma \etal,~\textit{Phys. Rev. B \textbf{89}, 081107 (2014)}] to perform a detailed study of the Anderson localization transition in three dimensions for the Box, Gaussian, Lorentzian, and Binary disorder distributions, and benchmark them with exact numerical results. Utilizing the nonlocal hybridization function and the momentum resolved typical spectra to characterize the localization transition in three...

Topics: Disordered Systems and Neural Networks, Condensed Matter

Source: http://arxiv.org/abs/1505.02825

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Jun 28, 2018
06/18

by
Matteo Lulli; Giorgio Parisi; Andrea Pelissetto

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We present a new dynamic off-equilibrium method for the study of continuous transitions, which represents a dynamic generalization of the usual equilibrium cumulant method. Its main advantage is that critical parameters are derived from numerical data obtained much before equilibrium has been attained. Therefore, the method is particularly useful for systems with long equilibration times, like spin glasses. We apply it to the three-dimensional Ising spin-glass model, obtaining accurate...

Topics: Disordered Systems and Neural Networks, Condensed Matter

Source: http://arxiv.org/abs/1509.07814

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7.0

Jun 28, 2018
06/18

by
Atanu Nandy; Arunava Chakrabarti

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We present an analytically exact scheme of unraveling a multitude of flat, dispersionless photonic bands in a kagome waveguide strip where each elementary plaquette hosts a deterministic fractal geometry of arbitrary size. The number of non-dispersive eigenmodes grows as higher and higher order fractal geometry is embedded in the kagome motif. Such eigenmodes are found to be localized with finite support in the kagome strip and exhibit a hierarchy of localization areas. The onset of...

Topics: Disordered Systems and Neural Networks, Condensed Matter

Source: http://arxiv.org/abs/1511.06115

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Jun 29, 2018
06/18

by
S. Gattenloehner; I. V. Gornyi; P. M. Ostrovsky; B. Trauzettel; A. D. Mirlin; M. Titov

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We study transport properties of graphene with anisotropically distributed on-site impurities (adatoms) that are randomly placed on every third line drawn along carbon bonds. We show that stripe states characterized by strongly suppressed back-scattering are formed in this model in the direction of the lines. The system reveals L\'evy-flight transport in stripe direction such that the corresponding conductivity increases as the square root of the system length. Thus, adding this type of...

Topics: Disordered Systems and Neural Networks, Condensed Matter

Source: http://arxiv.org/abs/1604.07623

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7.0

Jun 29, 2018
06/18

by
Alexander Kuczala; Tatyana O. Sharpee

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Using the diagrammatic method, we derive a set of self-consistent equations that describe eigenvalue distributions of large correlated asymmetric random matrices. The matrix elements can have different variances and be correlated with each other. The analytical results are confirmed by numerical simulations. The results have implications for the dynamics of neural and other biological networks where plasticity induces correlations in the connection strengths within the network. We find that the...

Topics: Disordered Systems and Neural Networks, Condensed Matter

Source: http://arxiv.org/abs/1610.09353