From integrability to chaos in quantum Liouvillians

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.

Submission to SciPost Physics Core

References in corpus (6)

• Localization of interacting fermions at high temperature
• Semiclassical Foundation of Universality in Quantum Chaos
• Universal Signature from Integrability to Chaos in Dissipative Open Quantum Systems
• Periodic-orbit theory of universal level correlations in quantum chaos
• Dissipative phase transitions: Independent versus collective decay and spin squeezing
• Spacing ratio characterization of the spectra of directed random networks

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