Correspondence principle, dissipation, and Ginibre ensemble

TL;DR

This paper investigates the limits of the correspondence principle linking quantum chaos and classical chaotic motion via Ginibre ensemble spectral correlations, revealing that this connection fails even in prototypical dissipative systems.

Contribution

It systematically explores the correspondence principle in a dissipative kicked quantum system, showing its failure in the semiclassical limit and challenging its universality as a diagnostic of quantum chaos.

Findings

Ginibre spectral correlations are not a universal marker of dissipative quantum chaos.

The correspondence principle breaks down even in the semiclassical limit of the studied system.

Previous assumptions about the robustness of spectral diagnostics are challenged.

Abstract

The correspondence between quantum and classical behavior has been essential since the advent of quantum mechanics. This principle serves as a cornerstone for understanding quantum chaos, which has garnered increased attention due to its strong impact in various theoretical and experimental fields. When dissipation is considered, quantum chaos takes concepts from isolated quantum chaos to link classical chaotic motion with spectral correlations of Ginibre ensembles. This correspondence was first identified in periodically kicked systems with damping, but it has been shown to break down in dissipative atom-photon systems [Phys. Rev. Lett. 133, 240404 (2024)]. In this contribution, we revisit the original kicked model and perform a systematic exploration across a broad parameter space, reaching a genuine semiclassical limit. Our results demonstrate that the correspondence principle, as defined through this spectral connection, fails even in this prototypical system. These findings provide conclusive evidence that Ginibre spectral correlations are neither a robust nor a universal diagnostic of dissipative quantum chaos.