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Random matrix theory for quantum and classical metastability in local Liouvillians

Li, Jimin L; Rose, Dominic C; Garrahan, Juan P.; Luitz, David J

Random matrix theory for quantum and classical metastability in local Liouvillians Thumbnail


Authors

Jimin L Li

Dominic C Rose

David J Luitz



Abstract

We consider the effects of strong dissipation in quantum systems with a notion of locality, which induces a hierarchy of many-body relaxation timescales as shown in [Phys. Rev. Lett. 124, 100604 (2020)]. If the strength of the dissipation varies strongly in the system, additional separations of timescales can emerge, inducing a manifold of metastable states, to which observables relax first, before relaxing to the steady state. Our simple model, involving one or two "good" qubits with dissipation reduced by a factor α < 1 compared to the other "bad" qubits, confirms this picture and admits a perturbative treatment. Introduction-Quantum many-body systems are generically complex, and obtaining an analytic understanding of the position of all spectral resonances is often hopeless. It was realized early on [1-6] that this complexity is in fact so great that many statistical properties of the spectrum are identical with those of random matrices sampled from an ensemble determined by the symmetry of the system. These pioneering observations have been subsequently refined, resulting in cornerstones of our understanding of thermalization in unitary quantum many-body systems by virtue of the eigenstate thermalization hypothesis [7-14], only with exceptions in integrable [15-18], many-body localized [19-29], time-crystalline [30-32] or scarred and constrained systems [33-35].

Citation

Li, J. L., Rose, D. C., Garrahan, J. P., & Luitz, D. J. (2022). Random matrix theory for quantum and classical metastability in local Liouvillians. Physical Review B, 105(18), Article L180201. https://doi.org/10.1103/physrevb.105.l180201

Journal Article Type Article
Acceptance Date Apr 20, 2022
Online Publication Date May 6, 2022
Publication Date May 1, 2022
Deposit Date Apr 21, 2022
Publicly Available Date May 1, 2022
Journal Physical Review B
Print ISSN 2469-9950
Electronic ISSN 2469-9969
Publisher American Physical Society
Peer Reviewed Peer Reviewed
Volume 105
Issue 18
Article Number L180201
DOI https://doi.org/10.1103/physrevb.105.l180201
Public URL https://nottingham-repository.worktribe.com/output/7784336
Publisher URL https://journals.aps.org/prb/abstract/10.1103/PhysRevB.105.L180201
Additional Information ©2022 American Physical Society

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