相关论文: Universal spectral correlations in open Floquet sy…
In these two lectures given at the 1997 Zakopane workshop on "New Developments in Quantum Field Theory" we review recent results on universal fluctuations in QCD Dirac spectra. We start the first lecture with a review of some general…
We prove multi-dimensional central limit theorems for the spectral moments (of arbitrary degrees) associated with random matrices with real-valued i.i.d. entries, satisfying some appropriate moment conditions. Our techniques rely on a…
A generalisation of the Ginibre ensemble of non-Hermitian random square matrices is introduced. The corresponding probability measure is induced by the ensemble of rectangular Gaussian matrices via a quadratisation procedure. We derive the…
We study the spectral properties of a multiparametric system having particle-hole symmetry in random matrix setting. We observe a crossover from Poisson to Wigner-Dyson like behavior in average local ratio of spacing within a spectrum of…
Entanglement entropy is a powerful tool in characterizing universal features in quantum many-body systems. In quantum chaotic Hermitian systems, typical eigenstates have near maximal entanglement with very small fluctuations. Here, we show…
We study the $n$-level spectral correlation functions of classically chaotic quantum systems without time-reversal symmetry. According to Bohigas, Giannoni and Schmit's universality conjecture, it is expected that the correlation functions…
We consider the complex eigenvalues of the induced spherical Ginibre ensemble with symplectic symmetry and establish the local universality of these point processes along the real axis. We derive scaling limits of all correlation functions…
We investigate coherent multiple scattering effects in the random quantum kicked rotor model. By changing the starting time of the Floquet period, two new classes of models can be introduced that exhibit similar interference structures. For…
Non-Hermitian random matrices with statistical spectral characteristics beyond the standard Ginibre ensembles have recently emerged in the description of dissipative quantum many-body systems as well as in non-ergodic wave transport in…
Consider $N\times N$ Hermitian or symmetric random matrices $H$ where the distribution of the $(i,j)$ matrix element is given by a probability measure $\nu_{ij}$ with a subexponential decay. Let $\sigma_{ij}^2$ be the variance for the…
The spectral properties of interacting strongly chaotic systems are investigated for growing interaction strength. A very sensitive transition from Poisson statistics to that of random matrix theory is found. We introduce a new random…
Random matrices from the elliptic Ginibre orthogonal ensemble (GinOE) are a certain linear combination of a real symmetric, and real anti-symmetric, real Gaussian random matrices and controlled by a parameter $\tau$. Our interest is in the…
Spectral correlations are a powerful tool to study the dynamics of quantum many-body systems. For Hermitian Hamiltonians, quantum chaotic motion is related to random matrix theory spectral correlations. Based on recent progress in the…
Local composition fluctuations in random alloys become crucial when one or more dimensions are reduced to the nanoscale. Using extended H\"uckel theory, we study the semiconductor random alloy SiGe sandwiched between Si due to its relevance…
We investigate the spectral properties of all-to-all interacting spin Hamiltonians acting on exactly $k$ spins, whose coupling coefficients are drawn from a normal distribution with mean $\mu$ and variance $\sigma^2$. For $\mu = 0$, we…
The spectral fluctuations of complex quantum systems, in appropriate limit, are known to be consistent with that obtained from random matrices. However, this relation between the spectral fluctuations of physical systems and random matrices…
Random contractions (sub-unitary random matrices) appear naturally when considering quantized chaotic maps within a general theory of open linear stationary systems with discrete time. We analyze statistical properties of complex…
We investigate singular value statistics for products of independent rectangular complex Ginibre matrices. When the rectangularity parameters of the matrices converge to a common limit in the asymptotic regime, the limiting spectral density…
To treat the spectral statistics of quantum maps and flows that are fully chaotic classically, we use the rigorous Riemann-Siegel lookalike available for the spectral determinant of unitary time evolution operators $F$. Concentrating on…
We review our recent works on the dynamical localization in the quantum kicked rotator (QKR) and the related properties of the classical kicked rotator (the standard map, SM). We introduce the Izrailev $N$-dimensional model of the QKR and…