Related papers: The L\'evy-Rosenzweig-Porter random matrix ensembl…
In this article the statistical properties of symmetrical random matrices whose elements are drawn from a q-parametrized non-extensive statistics power-law distribution are investigated. In the limit as q->1 the well known Gaussian…
The generalized Rosenzweig-Porter model with real (GOE) off-diagonal entries arguably constitutes the simplest random matrix ensemble displaying a phase with fractal eigenstates, which we characterize here by using replica methods. We first…
We study sample-to-sample fluctuations of the gap ratio in the energy spectra in finite disordered spin chains. The chains are described by the random-field Ising model and the Heisenberg model. We show that away from the ergodic/nonergodic…
We study analytically and numerically the dynamics of the generalized Rosenzweig-Porter model, which is known to possess three distinct phases: ergodic, multifractal and localized phases. Our focus is on the survival probability $R(t)$, the…
The random banded matrices (RBM) whose diagonal elements fluctuate much stronger than the off-diagonal ones were introduced recently by Shepelyansky as a convenient model for coherent propagation of two interacting particles in a random…
We consider disordered tight-binding models which Green's functions obey the self-consistent cavity equations . Based on these equations and the replica representation, we derive an analytical expression for the fractal dimension D_{1} that…
The distribution of the ratios of consecutive eigenvalue spacings of random matrices has emerged as an important tool to study spectral properties of many-body systems. This article numerically investigates the eigenvalue ratios…
We report on experimental studies of the distribution of the off-diagonal elements of the scattering matrix of open microwave networks with symplectic symmetry and a chaotic wave dynamics. These consist of two geometrically identical…
Matrix models showing chaotic-integrable transition in the spectral statistics are important for understanding Many Body Localization (MBL) in physical systems. One such example is the $\beta$-ensemble, known for its structural simplicity.…
Using the theory of free random variables (FRV) and the Coulomb gas analogy, we construct stable random matrix ensembles that are random matrix generalizations of the classical one-dimensional stable L\'{e}vy distributions. We show that the…
We report on an experimental investigation of the transition of a quantum system with integrable classical dynamics to one with violated time-reversal (T) invariance and chaotic classical counterpart. High-precision experiments are…
We investigate the propagation of waves in one-dimensional systems with L\'evy-type disorder. We perform a complete analysis of non-relativistic and relativistic wave transmission submitted to potential barriers whose width, separation or…
In this work, we study some statistical properties of the extreme eigenstates of the randomly-weighted adjacency matrices of random graphs. We focus on two random graph models: Erd\H{o}s-R\'{e}nyi (ER) graphs and random geometric graphs…
What is the analogue of L\'evy processes for random surfaces? Motivated by scaling limits of random planar maps in random geometry, we introduce and study L\'evy looptrees and L\'evy maps. They are defined using excursions of general L\'evy…
The Rosenzweig-Porter model is a one-parameter family of random matrices with three different phases: ergodic, extended non-ergodic and localized. We characterize numerically each of these phases and the transitions between them. We focus…
Fractal dimensions are tools for probing the structure of quantum states and identifying whether they are localized or delocalized in a given basis. These quantities are commonly extracted through finite-size scaling, which limits the…
Recent work has proposed fading ergodicity as a mechanism for many-body ergodicity breaking. Here, we show that two paradigmatic random matrix ensembles -- the Rosenzweig-Porter model and the ultrametric model -- fall within the same…
We study the reduced energy spectrum $\{E_{i}^{(n)}\}$, which is constructed by picking one level from every $n$ levels of the original spectrum $\{E_{i}\}$, in a Gaussian ensemble of random matrix with Dyson index $\beta\in \left( 0,\infty…
In this paper we give a physically transparent picture of singular-continuous spectrum in disordered systems which possess a non-ergodic extended phase. We present a simple model of identically and independently distributed level spacing in…
We use the Random Matrix Theory (RMT) to study the probability distribution function and moments of the wave power transmitted inside systems with ergodic wave motion. The results describe either open multichannel systems or their closed…