Journal
PHYSICAL REVIEW E
Volume 92, Issue 4, Pages -Publisher
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevE.92.042143
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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 cannot be larger than similar to 1/L. In integrable systems with boundary dissipation one typically observes scaling of similar to 1/L-3, while in chaotic ones one can have faster relaxation with the gap scaling as similar to 1/L and thus saturating the generic bound. We also observe transition from exponential to algebraic gap in systems with localized modes.
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