Related papers: Delocalization-Localization Transition due to Anha…
We address the question of the effect of disorder on heat conduction in an anharmonic chain with interactions given by the Fermi-Pasta-Ulam (FPU) potential. In contrast to the conclusions of an earlier paper [Phys. Rev. Lett. 86, 63 (2001)]…
The equilibration of sinusoidally modulated distribution of the kinetic temperature is analyzed in the $\beta$-Fermi-Pasta-Ulam-Tsingou chain with different degrees of nonlinearity and for different wavelengths of temperature modulation.…
We show that many-body localization, which exists in tight-binding models, is unstable in a continuum. Irrespective of the dimensionality of the system, many-body localization does not survive the unbounded growth of the single-particle…
The transition from a many-body localized phase to a thermalizing one is a dynamical quantum phase transition which lies outside the framework of equilibrium statistical mechanics. We provide a detailed study of the critical properties of…
We present a numerical study of dynamical correlations (structure factors) of the long-range generalization of the Fermi-Pasta-Ulam oscillator chain, where the strength of the interaction between two lattice sites decays as a power $\alpha$…
We numerically analyze the energy level statistics of the Anderson model with Gaussian site disorder and constant hopping. The model is realized on different two-dimensional lattices, namely, the honeycomb, the kagom\'e, the square, and the…
We study, theoretically and numerically, a minimal model for phonons in a disordered system. For sufficient disorder, the vibrational modes of this classical system can become Anderson localized, yet this problem has received significantly…
Discrete breathers are time-periodic, spatially localized solutions of the equations of motion for a system of classical degrees of freedom interacting on a lattice. Such solutions are investigated for a diatomic Fermi-Pasta-Ulam chain, i.…
In this note we prove the existence of a localization/delocalization transition for Landau Hamiltonians randomly perturbed by an electric potential with unbounded amplitude. In particular, with probability one, no Landau gaps survive as the…
The recently discovered phenomenon of nonlinear supratransmission consists in a sudden increase of the amplitude of a transmitted wave triggered by the excitation of nonlinear localized modes of the medium. We examine this process for the…
The intensity distribution of electromagnetic polar waves in a chain of near-resonant weakly-coupled scatterers is investigated theoretically and supported by a numerical analysis. Critical scaling behavior is discovered for part of the…
We establish rigorous bounds on the decorrelation time and thermal transport in the disordered Klein-Gordon chain with a quartic on-site potential, governed by a parameter $\lambda$. At $\lambda = 0$, the chain is harmonic, and any form of…
The evolution towards equipartition in the $\beta$-FPU chain is studied considering as initial condition the highest frequency mode. Above an analytically derived energy threshold, this zone-boundary mode is shown to be modulationally…
Several systems display an equilibrium condensation transition, where a finite fraction of a conserved quantity is spatially localized. The presence of two conservation laws may induce the emergence of such transition in an…
The energy transition towards an increased supply of renewable energy raises concerns that existing electricity grids, built to connect few centralized large power plants with consumers, may become more difficult to control and stabilized…
We study the dynamics of Fermi-Pasta-Ulam chains with both harmonic and anharmonic power-law long-range interactions. We show that the dynamics is described in the continuum limit by a generalized fractional Boussinesq differential…
We formulate a theory of the many-body localization transition based on a novel real space renormalization group (RG) approach. The results of this theory are corroborated and intuitively explained with a phenomenological effective…
We study the energy transfer in a classical dipole chain of $N$ interacting rigid rotating dipoles. The underlying high--dimensional potential energy landscape is analyzed in particular by determining the equilibrium points and their…
This paper presents the first experimental evidence of the transition from dynamical localization to delocalization under the influence of a quasi-periodic driving on a quantum system. A quantum kicked rotator is realized by placing cold…
A weakly disordered quasi-one-dimensional tight-binding hopping model with $N$ rows is considered. The probability distribution of the Landauer conductance is calculated exactly in the middle of the band, $\epsilon=0$, and it is shown that…