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From integrability to chaos in quantum Liouvillians

by Álvaro Rubio-García, Rafael A. Molina, Jorge Dukelsky

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Submission summary

Authors (as registered SciPost users): Rafael Molina · Alvaro Rubio-García
Submission information
Preprint Link: scipost_202110_00003v2  (pdf)
Date accepted: 2022-03-24
Date submitted: 2022-03-10 11:01
Submitted by: Rubio-García, Alvaro
Submitted to: SciPost Physics Core
Ontological classification
Academic field: Physics
  • Dynamical Systems
  • Condensed Matter Physics - Experiment
  • Condensed Matter Physics - Theory
  • Quantum Physics
  • Statistical and Soft Matter Physics
Approaches: Theoretical, Computational


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.

List of changes

- In the discussion of the F operator above Eq. (8) we now explicitly mention it is an anti-unitary operator and refer to it as an operator instead of as a weak symmetry.

- In the new version of the manuscript we now explain below Eq. (16) the reasons that lead us to choose n_j ~ L/2, mainly that introducing as many (orthonormal) random jumps as number of spins leads again to a diagonal - and thus integrable - Liouvillian.

- We fixed above Eq. (12): "the set integrable Liouvillians" -> "the set of integrable Liouvillians"

Published as SciPost Phys. Core 5, 026 (2022)

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