A Method to Modify RMT using Short-Time Behavior in Chaotic Systems

TL;DR

This paper introduces a method to modify Random Matrix Theory eigenstate statistics by incorporating short-time dynamics, improving accuracy in chaotic systems without requiring Hamiltonian diagonalization.

Contribution

The authors present a novel approach that accounts for non-universal short-time behavior in chaotic systems, bridging the gap between RMT and actual dynamics.

Findings

Improved accuracy in wave function autocorrelations and cross-correlations

Method recovers RMT and semiclassical limits under specific conditions

Avoids Hamiltonian diagonalization by using short-time dynamics

Abstract

We discuss a modification to Random Matrix Theory eigenstate statistics, that systematically takes into account the non-universal short-time behavior of chaotic systems. The method avoids diagonalization of the Hamiltonian, instead requiring only a knowledge of short-time dynamics for a chaotic system or ensemble of similar systems. Standard Random Matrix Theory and semiclassical predictions are recovered in the limits of zero Ehrenfest time and infinite Heisenberg time, respectively. As examples, we discuss wave function autocorrelations and cross-correlations, and show how the approach leads to a significant improvement in accuracy for simple chaotic systems where comparison can be made with brute-force diagonalization.