Full perturbative calculation of spectral correlation functions for chaotic systems in the unitary symmetry class

TL;DR

This paper performs a comprehensive perturbative calculation of spectral correlation functions for quantum chaotic systems in the unitary class, confirming universality and introducing an exactly solvable auxiliary matrix model.

Contribution

It provides an all-orders perturbative derivation of spectral correlations in the unitary class using a novel auxiliary matrix model.

Findings

Off-diagonal contributions cancel in spectral correlations.

Universality of spectral correlation functions is confirmed.

An exactly solvable matrix model underpins the semiclassical approach.

Abstract

Starting from a semiclassical approach recently developed for spectral correlation functions of quantum systems whose classical dynamics is chaotic, we focus on the case of broken time-reversal symmetry, the so-called unitary class. We obtain to all orders in perturbation theory the non-oscillatory parts of all correlation functions, showing that the off-diagonal contributions to these correlation functions cancel and the conjectured universailty holds. The innovation that allows this calculation to be performed is the introduction of an auxiliary matrix model which is governed by the same diagrammatic rules as the semiclassical approach and which can be exactly solved.