Beyond the Heisenberg time: Semiclassical treatment of spectral correlations in chaotic systems with spin 1/2

TL;DR

This paper develops a semiclassical approach to analyze spectral correlations in chaotic systems with spin 1/2, extending the understanding of spectral form factors beyond the Heisenberg time and confirming their agreement with random matrix theory predictions.

Contribution

It introduces a semiclassical method to evaluate spectral correlations in spin-1/2 chaotic systems and establishes a duality between orthogonal and symplectic symmetry classes.

Findings

Spectral form factor matches Gaussian symplectic ensemble predictions.

Duality between orthogonal and symplectic generating functions is demonstrated.

Method extends spectral analysis beyond the Heisenberg time.

Abstract

The two-point correlation function of chaotic systems with spin 1/2 is evaluated using periodic orbits. The spectral form factor for all times thus becomes accessible. Equivalence with the predictions of random matrix theory for the Gaussian symplectic ensemble is demonstrated. A duality between the underlying generating functions of the orthogonal and symplectic symmetry classes is semiclassically established.