相关论文: Random Matrix Theory of Resonances: an Overview
We check the eigenvalue spectrum of the $\Phi^{4}_{1+1}$ Hamiltonian against Poisson or Wigner behavior predicted from random matrix theory. We discuss random matrix theory as a tool to discriminate the validity of a model Hamiltonian…
We address the quantum-classical correspondence for chaotic systems with a crossover between symmetry classes. We consider the energy level statistics of a classically chaotic system in a weak magnetic field. The generating function of…
The statistics of gaps between quantum energy levels is a hallmark criterion in quantum chaos and quantum integrability studies. The relevant distributions corresponding to exactly integrable vs. fully chaotic systems are universal and…
Distributions of eigenmodes are widely concerned in both bounded and open systems. In the realm of chaos, counting resonances can characterize the underlying dynamics (regular vs. chaotic), and is often instrumental to identify…
The purpose of this review article is to present some of the latest developments using random techniques, and in particular, random matrix techniques in quantum information theory. Our review is a blend of a rather exhaustive review,…
We apply random-matrix-theory (RMT) to the analysis of evolution of wavepackets in energy space. We study the crossover from ballistic behavior to saturation, the possibility of having an intermediate diffusive behavior, and the feasibility…
This thesis addresses two persistent and closely related challenges in modern deep learning, reliability and efficiency, through a unified framework grounded in Spectral Geometry and Random Matrix Theory (RMT). As deep networks and large…
We present a systematic construction of probes into the dynamics of isospectral ensembles of Hamiltonians by the notion of Isospectral twirling, expanding the scopes and methods of ref.[1]. The relevant ensembles of Hamiltonians are those…
Using random matrix technique we determine an exact relation between the eigenvalue spectrum of the covariance matrix and of its estimator. This relation can be used in practice to compute eigenvalue invariants of the covariance…
The statistics of the nodal lines and nodal domains of the eigenfunctions of quantum billiards have recently been observed to be fingerprints of the chaoticity of the underlying classical motion by Blum et al. (Phys. Rev. Lett., Vol. 88…
We propose a random matrix modeling for the parametric evolution of eigenstates. The model is inspired by a large class of quantized chaotic systems. Its unique feature is having parametric invariance while still possessing the…
Problem of long-range sound propagation in the randomly-inhomogeneous deep ocean is considered. We examine a novel approach for modeling of wave propagation, developed by K.C.Hegewisch and S.Tomsovic. This approach relies on construction of…
We assume that the level spectra of quantum systems in the initial phase of transition from integrability to chaos are approximated by superpositions of independent sequences. Each individual sequence is modeled by a random matrix ensemble.…
Multivariate statistical analysis is concerned with observations on several variables which are thought to possess some degree of inter-dependence. Driven by problems in genetics and the social sciences, it first flowered in the earlier…
Random matrix theory allows one to deduce the eigenvalue spectrum of a large matrix given only statistical information about its elements. Such results provide insight into what factors contribute to the stability of complex dynamical…
The quantum mechanical equivalent of parametric resonance is studied. A simple model of a periodically kicked harmonic oscillator is introduced which can be solved exactly. Classically stable and unstable regions in parameter space are…
Spectral statistics and correlations are the usual way to study the presence or absence of quantum chaos in quantum systems. We present our investigation on the study of the fluctuation average and variance of certain correlation functions…
In this paper we discuss in detail a numerical method to study resonances in membranes generated by domain walls in Randall-Sundrum-like scenarios. It is based on similar works to understand the quantum mechanics of electrons subject to the…
The multichannel generalization of the theory of spectral, scattering and decay control is presented. New universal algorithms of construction of complex quantum systems with given properties are suggested. Particularly, transformations of…
We study the effects of an arbitrary external perturbation in the statistical properties of the S-matrix of quantum chaotic scattering systems in the limit of isolated resonances. We derive, using supersymmetry, an exact non-perturbative…