Žnidarič Marko
Physics Department, Faculty of Mathematics and Physics, University of Ljubljana, Ljubljana, Slovenia.
Phys Rev E Stat Nonlin Soft Matter Phys. 2015 Oct;92(4):042143. doi: 10.1103/PhysRevE.92.042143. Epub 2015 Oct 20.
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 ∼1/L. In integrable systems with boundary dissipation one typically observes scaling of ∼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.
我们研究由林德布拉德主方程描述的量子多体系统的弛豫时间，也称为混合时间。我们特别研究能隙随系统长度的标度，即所谓的动力学指数，确定标度中的一些转变。对于具有体耗散的系统，我们通常观察到小耗散强度和强耗散强度下不同的标度，在热力学极限下临界转变强度趋于零。我们还研究了最大衰减模式中的相关相变。对于仅具有边界耗散的系统，我们给出了一个一般的界限，即能隙不能大于 ∼1/L。在具有边界耗散的可积系统中，通常观察到 ∼1/L(3) 的标度，而在混沌系统中，能隙标度为 ∼1/L 时弛豫可能更快，从而达到一般界限饱和。我们还观察到具有局域模式的系统中从指数能隙到代数能隙的转变。
