From integrability to chaos in quantum Liouvillians

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...

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Bibliographic Details
Published inSciPost physics core Vol. 5; no. 2; p. 026
Main Authors Rubio-García, Alvaro, Molina, Rafael, Dukelsky, Jorge
Format Journal Article
LanguageEnglish
Published SciPost 01.04.2022
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Summary: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.
ISSN:2666-9366
2666-9366
DOI:10.21468/SciPostPhysCore.5.2.026