RIKEN Center for Emergent Matter Science (CEMS), Wako 351-0198, Japan.
Department of Computer Science and Communications Engineering, Waseda University, Tokyo 169-8555, Japan.
Phys Rev Lett. 2023 Jun 9;130(23):230404. doi: 10.1103/PhysRevLett.130.230404.
Markovian open quantum systems display complicated relaxation dynamics. The spectral gap of the Liouvillian characterizes the asymptotic decay rate toward the steady state, but it does not necessarily give a correct estimate of the relaxation time because the crossover time to the asymptotic regime may be too long. We here give a rigorous upper bound on the transient decay of autocorrelation functions in the steady state by introducing the symmetrized Liouvillian gap. The standard Liouvillian gap and the symmetrized one are identical in an equilibrium situation but differ from each other in the absence of the detailed balance condition. It is numerically shown that the symmetrized Liouvillian gap always gives a correct upper bound on the decay of the autocorrelation function, but the standard Liouvillian gap does not.
马科夫开放量子系统呈现出复杂的弛豫动力学。李雅普诺夫的谱隙表征了向稳态的渐近衰减率，但它不一定能正确估计弛豫时间，因为过渡到渐近状态的时间可能太长。我们通过引入对称李雅普诺夫隙，给出了在稳态下自相关函数瞬态衰减的严格上界。在平衡态下，标准李雅普诺夫隙和对称李雅普诺夫隙是相同的，但在没有详细平衡条件的情况下，它们是不同的。数值结果表明，对称李雅普诺夫隙总是能正确地给出自相关函数衰减的上界，而标准李雅普诺夫隙则不能。
