论文标题
马尔可夫开放量子系统中对称的liouvillian差距
Symmetrized Liouvillian Gap in Markovian Open Quantum Systems
论文作者
论文摘要
Markovian开放量子系统显示复杂的松弛动力学。 liouvillian的光谱间隙表征了渐近状态的渐近衰减速率，但不一定给出了对放松时间的正确估计，因为渐近状态的交叉时间可能太长了。我们在这里通过引入对称的liouvillian间隙，在稳态的自动相关函数的瞬态衰减上给出了严格的上限。标准的liouvillian间隙和对称的差距在平衡情况下是相同的，但在没有详细的平衡条件的情况下彼此不同。从数值上表明，对称的liouvillian间隙始终在自动相关函数的衰减上给出正确的上限，但是标准的liouvillian间隙却没有。
Markovian open quantum systems display complicated relaxation dynamics. The spectral gap of the Liouvillian characterizes the asymptotic decay rate towards 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 auto-correlation 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 give a correct upper bound on the decay of the auto-correlation function, but the standard Liouvillian gap does not.
