Ergodic and chaotic properties in Tavis-Cummings dimer: quantum and classical limit

TL;DR

This paper explores the ergodic and chaotic behaviors of the Tavis-Cummings dimer system, analyzing quantum and classical dynamics, chaos indicators, and the transition between localized and delocalized states, with implications for quantum chaos and classical-quantum correspondence.

Contribution

It provides a detailed analysis of chaos, ergodicity, and quantum-classical correspondence in the Tavis-Cummings dimer, highlighting the transition from integrability to chaos and the role of random matrix theory.

Findings

Identification of chaotic and ergodic regimes via Lyapunov exponents

Demonstration of mixed quantum behavior using random matrix diagnostics

Analysis of chaos in open quantum systems and connections to non-Hermitian matrices

Abstract

We investigate two key aspects of quantum systems by using the Tavis-Cummings dimer system as a platform. The first aspect involves unraveling the relationship between the phenomenon of self-trapping (or lack thereof) and integrability (or quantum chaos). Secondly, we uncover {the possibility of} mixed behavior in this quantum system using diagnostics based on random matrix theory and make an in-depth study of classical-quantum correspondence. The setup chosen for the study is precisely suited as it (i) enables a transition from delocalized to self-trapped states and (ii) has a well-defined classical limit, thereby amenable to studies involving classical-quantum conjectures. The obtained classical model in itself has rich chaotic and ergodic properties which were probed via maximal Lyapunov exponents. Furthermore, we present aspects of chaos in the corresponding open quantum system and make connections with non-Hermitian random matrix theory.