Spatial Correlation in Quantum Chaotic Systems with Time-Reversal Symmetry: Theory and Experiment

Abstract

The correct Eqs. (20) and (21) read as follows:Q ab cdQ1982 0031-9007͞96͞76(11)͞1982(1)$10.00

Quantum chaos, random matrix theory, statistical mechanics in two dimensions, and the second law - a case study

“…An overwhelming number of numerical experiments on spectral statistics [3,4] and their corresponding semiclassical analysis [5,6] suggest that the universal features observed in chaotic quantum systems can be modelled in terms of random matrix theory. Apart from energy spectra, it has been found that the conjecture [7] where an eigenstate of a chaotic quantum system is represented as a Gaussian random superposition of plane waves entails results which are found in agreement with numerical studies [8,4]. We believe that an important step has been in establishing the result that this conjecture leads to momentum distribution of ideal gases, thus bringing out statistical mechanics [9].…”

“…As noted in [9], the higher-order even-point correlation functions factorize and the odd-ones vanish. A very important aspect of the ansatz (7), (8) is that the…”

“…The random pure state can be written (for the system we are considering) as (7,8) in three (or greater) space dimensions, or, as (13)(14)(15) in two dimensions. These equations can be interpreted as choosing a pure state at random for a specific choice of amplitude, A α .…”