Estudo termodinâmico de sistemas quânticos caóticos via Teoria de Matrizes Aleatórias

Abstract

Results from classical Random Matrix Theory (RMT) are well recognized as a way to describe spectral statistical properties of classically chaotic quantum systems, such as the level spacing distribution. We investigate, both numerically and analytically, if RMT can be used, at least for some regimes, to predict the behavior of the statistics of work performed by quenching some external parameter dictating the dynamics of a quantum chaotic system. This is done by comparison of the characteristic function of work obtained numerically from a well known quantum chaotic system called Dicke Model and from matrices pertaining to one of the classical ensembles of RMT, namely GOE. We also show one analytical result for the RMT average of the characteristic function that holds in the limit of high temperatures.