GSE statistics without spin

TL;DR

This paper introduces a new mechanism for obtaining Gaussian Symplectic Ensemble (GSE) statistics in quantum systems, based on geometric symmetries rather than spin, demonstrated through a quantum graph with quaternion symmetry.

Contribution

It presents an alternative to spin-based GSE statistics by using geometric symmetries, specifically quaternion group symmetry, in quantum graphs.

Findings

GSE statistics observed in a quantum graph with quaternion symmetry

GSE can arise without half-integer spin or time-reversal invariance

Symmetry-based approach broadens understanding of quantum chaos phenomena

Abstract

Energy levels statistics following the Gaussian Symplectic Ensemble (GSE) of Random Matrix Theory have been predicted theoretically and observed numerically in numerous quantum chaotic systems. However in all these systems there has been one unifying feature: the combination of half-integer spin and time-reversal invariance. Here we provide an alternative mechanism for obtaining GSE statistics that is based on geometric symmetries of a quantum system which alleviates the need for spin. As an example, we construct a quantum graph with a particular discrete symmetry given by the quaternion group Q8. GSE statistics is then observed within one of its subspectra.