2015/07/31 by Marko Znidaric · 2 citations
Physics and Astronomy · #cond-mat.stat-mech #quant-ph
paper · pdf · doi:10.1103/physreve.92.042143
published as Phys. Rev. E 92, 042143 (2015) · 18 pages; v2: additional explanation of exponentially small gap
arxiv created 2015/10/29 · arxiv updated 2015/10/30
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/L3, 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.