From integrability to chaos in quantum Liouvillians

TL;DR

This paper introduces a new class of integrable many-body Liouvillians derived from Richardson-Gaudin models and investigates the transition to chaos through spectral analysis of their eigenvalues.

Contribution

It presents a novel family of integrable open quantum system models based on Richardson-Gaudin structures and explores the integrability-chaos transition in these systems.

Findings

Identification of integrable Liouvillian models with complex jump operators

Spectral statistics reveal the transition from integrability to chaos

Eigenvalue spacing ratios characterize the chaos onset

Abstract

The dynamics of open quantum systems can be described by a Liouvillian, which in the Markovian approximation fulfills the Lindblad master equation. We present a family of integrable many-body Liouvillians based on Richardson-Gaudin models with a complex structure of the jump operators. Making use of this new region of integrability, we study the transition to chaos in terms of a two-parameter Liouvillian. The transition is characterized by the spectral statistics of the complex eigenvalues of the Liouvillian operators using the nearest neighbor spacing distribution and by the ratios between eigenvalue distances.