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.

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马尔可夫开放量子系统中的对称刘维尔能隙

马尔可夫开放量子系统表现出复杂的弛豫动力学。刘维尔的谱间隙表征了趋向稳态的渐近衰减率，但它不一定给出弛豫时间的正确估计，因为渐近状态的交叉时间可能太长。我们在这里通过引入对称刘维尔间隙给出了稳态下自相关函数瞬态衰减的严格上限。标准刘维尔间隙和对称间隙在平衡情况下是相同的，但在缺乏详细平衡条件时彼此不同。数值表明，对称刘维尔间隙总是给出自相关函数衰减的正确上限，但标准刘维尔间隙则不然。