Related papers: Difference between level statistics, ergodicity an…
At zero temperature the lowest part of the spectrum of the QCD Dirac operator is known to consist of delocalized modes that are described by random matrix statistics. In the present paper we show that the nature of these eigenmodes changes…
We study the Anderson model on the Bethe lattice by working directly with propagators at real energies $E$. We introduce a novel criterion for the localization-delocalization transition based on the stability of the population of the…
We study a classical model of thermally fluctuating polymers confined to two dimensions, experiencing a grooved periodic potential, and subject to pulling forces both along and transverse to the grooves. The equilibrium polymer…
We prove a result of delocalization for the Anderson model on the regular tree (Bethe lattice). When the disorder is weak, it is known that large parts of the spectrum are a.s. purely absolutely continuous, and that the dynamical transport…
Local observables in generic periodically driven closed quantum systems are known to relax to values described by periodic infinite temperature ensembles. At the same time, ergodic static systems exhibit anomalous thermalization of local…
Local entanglement between pairs of spins, as measured by concurrence, is investigated in a disordered spin model that displays a transition from an ergodic to a many-body localized phase in excited states. It is shown that the concurrence…
Using the level--spacing distribution and the total probability function of the numbers of levels in a given energy interval we analyze the crossover of the level statistics between the delocalized and the localized regimes. By numerically…
Critical behavior of solitonic waveforms of Bose-Einstein condensates in optical lattices (OL) has been studied in the framework of continuous mean-field equation. In 2D and 3D OLs bright matter-wave solitons undergo abrupt delocalization…
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.…
A theoretical model is presented, describing the glassy freezing of electrons in the vicinity of disorder driven metal-insulator transitions. Our results indicate that the onset of glassy dynamics should emerge before the localization…
One fundamental assumption in statistical physics is that generic closed quantum many-body systems thermalize under their own dynamics. Recently, the emergence of many-body localized systems has questioned this concept, challenging our…
The localisation of electrons in a lattice potential is an quantum-mechanical phenomenon and is often associated with remarkable physical properties of solids involving electron spins, electric polarisations and topological effects. In…
Experiments in Rydberg atoms have recently found unusually slow decay from a small number of special initial states. We investigate the robustness of such long-lived states (LLS) by studying an ensemble of locally constrained random systems…
Strongly disordered systems in the many-body localized (MBL) phase can exhibit ground state order in highly excited eigenstates. The interplay between localization, symmetry, and topology has led to the characterization of a broad landscape…
We study, at zero temperature, the dynamics of a single electron in a Holstein model augmented by site-diagonal, binary-alloy type disorder. The average over the phonon vacuum and the alloy configurations is performed within a generalized…
Recently, a metal-insulator transition (MIT) was found in the anisotropic Anderson model of localization by transfer-matrix methods (TMM). This MIT has been also investigated by multifractal analysis (MFA) and the same critical disorders…
We study the thermalization properties of a fully nonlinear lattice model originally derived from the two-dimensional cubic defocusing nonlinear Schr\"odinger equation (NLS) using analytical and numerical methods. Our analysis reveals both…
We demonstrate that the synchronization of a lattice of solid-state condensates when inter-site tunnelling is switched on, depends strongly on the weak local disorder. This finding is vital for implementation of condensate arrays as…
We consider continuous-time random walk models described by arbitrary sojourn time probability density functions. We find a general expression for the distribution of time-averaged observables for such systems, generalizing some recent…
We propose a multi-scale diagonalization scheme to study disordered one-dimensional chains, in particular the transition between many-body localization (MBL) and the ergodic phase, expected to be governed by resonant spots. Our scheme…