Accelerated Decay due to Operator Spreading in Bulk-Dissipated Quantum Systems

Abstract

Markovian open many-body quantum systems display complicated relaxation dynamics. The spectral gap of the Liouvillian characterizes the asymptotic decay rate towards the stationary state, but it has recently been pointed out that the spectral gap does not necessarily determine the overall relaxation time. Our understanding on the relaxation process before the asymptotically long-time regime is still limited. We here present a collective relaxation dynamics of autocorrelation functions in the stationary state. As a key quantity in the analysis, we introduce the instantaneous decay rate, which characterizes the transient relaxation and converges to the conventional asymptotic decay rate in the long-time limit. Our theory predicts that a bulk-dissipated system generically shows an accelerated decay before the asymptotic regime due to the scrambling of quantum information associated with the operator spreading.

5 pages, 3 figures (Supplemental Material 3 pages, 3 figures)

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Cited by in corpus (4)

• Integrability versus chaos in the steady state of many-body open quantum systems
• Open-system dynamics in local Lindbladians with chaotic spectra
• Dissipation- versus Chaos-Induced Relaxation in Non-Markovian Quantum Many-Body Systems
• Error bounds on the universal Lindblad equation in the thermodynamic limit