Random Wave Functions with boundary and normalization constraints: Quantum statistical physics meets quantum chaos

TL;DR

This paper introduces an enhanced random wave model that accounts for boundaries and normalization, linking quantum chaos and statistical physics through universal eigenfunction fluctuation behavior.

Contribution

It develops a refined Berry's ansatz incorporating boundary conditions and normalization, and reformulates the Random Wave conjecture to emphasize universality in chaotic quantum systems.

Findings

Enhanced random wave model with boundary and normalization constraints

Reformulation of the Random Wave conjecture emphasizing universality

Connection between quantum chaos and statistical physics through semiclassical methods

Abstract

We present an improved version of Berry's ansatz able to incorporate exactly the existence of boundaries and the correct normalization of the eigenfunction into an ensemble of random waves. We then reformulate the Random Wave conjecture showing that in its new version it is a statement about the universal nature of eigenfunction fluctuations in systems with chaotic classical dynamics. The emergence of the universal results requires the use of both semiclassical methods and a new expansion for a very old problem in quantum statistical physics