Relaxation times of dissipative many-body quantum systems

Abstract

We study relaxation times, also called mixing times, of quantum many-body systems described by a Lindblad master equation. We in particular study the scaling of the spectral gap with the system length, the so-called dynamical exponent, identifying a number of transitions in the scaling. For systems with bulk dissipation we generically observe different scaling for small and for strong dissipation strength, with a critical transition strength going to zero in the thermodynamic limit. We also study a related phase transition in the largest decay mode. For systems with only boundary dissipation we show a generic bound that the gap can not be larger than 1/L. In integrable systems with boundary dissipation one typically observes scaling 1/L^3, while in chaotic ones one can have faster relaxation with the gap scaling as 1/L and thus saturating the generic bound. We also observe transition from exponential to algebraic gap in systems with localized modes.

18 pages; v2: additional explanation of exponentially small gap

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