Dynamical Universal Behavior in Quantum Chaotic Systems

TL;DR

This paper demonstrates that quantum chaotic systems exhibit a universal exponential probability distribution for wave packet densities, contrasting with classical Gaussian distributions, and shows the transition between these distributions through coarse graining.

Contribution

It provides a rigorous proof that quantum chaotic systems universally have exponential density distributions, contrasting with classical Gaussian distributions, and explores the transition between them.

Findings

Quantum chaotic systems have exponential density distributions.

Classical systems exhibit Gaussian density distributions.

Transition from quantum to classical distribution via coarse graining.

Abstract

We discover numerically that a moving wave packet in a quantum chaotic billiard will always evolve into a quantum state, whose density probability distribution is exponential. This exponential distribution is found to be universal for quantum chaotic systems with rigorous proof. In contrast, for the corresponding classical system, the distribution is Gaussian. We find that the quantum exponential distribution can smoothly change to the classical Gaussian distribution with coarse graining.