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

TL;DR

This paper investigates the transient relaxation dynamics in bulk-dissipated quantum systems, revealing that operator spreading causes an accelerated decay before the system reaches its long-time asymptotic state.

Contribution

It introduces the instantaneous decay rate to analyze transient relaxation and demonstrates that operator spreading accelerates decay in bulk-dissipated quantum systems.

Findings

Transient decay is faster than asymptotic decay due to operator spreading.

The instantaneous decay rate converges to the asymptotic rate at long times.

Bulk dissipation leads to accelerated relaxation in 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.