Accelerated Decay due to Operator Spreading in Bulk-Dissipated Quantum Systems
arxiv(2023)
摘要
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.
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