Related papers: Disordered statistical physics in low dimensions: …
We study the spectral statistics of interacting spinless fermions in a two-dimensional disordered lattice. Within a full quantum treatment for small few-particle-systems, we compute the low-energy many-body states numerically. While at weak…
Motivated by the problem of Many-Body Localization and the recent numerical results for the level and eigenfunction statistics on the random regular graphs, a generalization of the Rosenzweig-Porter random matrix model is suggested that…
Localization phenomena permeate many branches of physics playing a fundamental role on dynamical processes evolving on heterogeneous networks. These localization analyses are frequently grounded, for example, on eigenvectors of adjacency or…
It is widely believed that many-body localisation in one dimension is fragile and can be easily destroyed by thermal inclusions, however there are still many open questions regarding the stability of the localised phase and under what…
Nonequilibrium statistical mechanics exhibit a variety of complex phenomena far from equilibrium. It inherits challenges of equilibrium, including accurately describing the joint distribution of a large number of configurations, and also…
We study several lattice random walk models with stochastic resetting to previously visited sites which exhibit a phase transition between an anomalous diffusive regime and a localization regime where diffusion is suppressed. The localized…
We study the localization phenomena in a one-dimensional lattice system with a uniformly moving disordered potential. At a low moving velocity, we find a sliding localized phase in which the initially localized matter wave adiabatically…
We examine quantum percolation on a square lattice with random dilution up to $q=38%$ and energy $0.001 \le E \le 1.6$ (measured in units of the hopping matrix element), using numerical calculations of the transmission coefficient at a much…
We analyze the recently discovered localized and non-uniform phases of the Banks-Fischler-Shenker-Susskind (BFSS) matrix quantum mechanics. Building on [1], we provide first-principles derivations of their properties and extend the results…
We seek the possibility of a disorder driven transition in a tight-binding lattice with a flat band using complexity parameter approach. Our results indicate the existence of a localized to extended states transition with increasing…
The one dimensional dimer model is investigated and the localization length calculated exactly. The presence of delocalized states at $E_c = \epsilon_{a,b}$ of two possible values of the chemical potential in case of…
The energy level statistics of uniform random graphs are studied, by treating the graphs as random tight-binding lattices. The inherent random geometry of the graphs and their dynamical spatial dimensionality, leads to various quantum…
We explore order in low angle grain boundaries (LAGBs) embedded in a two-dimensional crystal at thermal equilibrium. Symmetric LAGBs subject to a periodic Peierls potential undergo, with increasing temperatures, a thermal depinning…
We study the effect of the competition between disorder and stress enhancement in fracture processes using the local load sharing fiber bundle model, a model that hovers on the border between analytical tractability and numerical…
We investigate the statistical properties of the eigenvalues and eigenvectors in a random matrix ensemble with $H_{ij}\sim |i-j|^{-\mu}$. It is known that this model shows a localization-delocalization transition (LDT) as a function of the…
In this paper, the development of a mathematical method is presented to explore spatially non-uniform phases with no long-range order in mathematical models of first order phase transitions. We use essential results regarding the…
A central theoretical issue at the core of the current research on many-body localization (MBL) consists in characterizing the statistics of rare long-range resonances in many-body eigenstates. This is of paramount importance to understand:…
It has been widely believed that almost all states in one-dimensional (1d) disordered systems with short-range hopping and uncorrelated random potential are localized. Here, we consider the fate of these localized states by coupling between…
We demonstrate that a weak disorder in atomic positions introduces spatially localized optical modes in a dense three-dimensional ensemble of immobile two-level atoms arranged in a diamond lattice and coupled by the electromagnetic field.…
These lecture notes give a pedagogical introduction to phase transitions in disordered quantum systems and to the exotic Griffiths phases induced in their vicinity. We first review some fundamental concepts in the physics of phase…