论文标题
liouvillian皮肤效应：放松过程放慢而没有差距闭合
Liouvillian Skin Effect: Slowing Down of Relaxation Processes without Gap Closing
论文作者
论文摘要
高度非凡的程度在多大程度上可以从liouvillian的光谱间隙中推断出量子耗散系统的松弛行为，该频谱差距控制密度矩阵的时间演变。我们研究了表现出Liouvillian皮肤效应的量子耗散系统的放松过程，这意味着Liouvillian的特征模式在指数上局部靠近系统边界，并发现该系统的时间表不仅取决于Liouvillian Gap $δ$δ$δ$ quig $ nbige $ em ex $ em ex $ c $ c $ sod $ cig $ cop $ ed $ c。特别是，我们表明，最大的放松时间$τ$在初始状态和本地可观察物中由$τ\simΔ^{ - 1}（1+l/ξ）$带有$ l $是系统大小。这意味着最长的放松时间可以在$ l \ to \ infty $的情况下差异，而无需闭合。
It is highly nontrivial to what extent we can deduce the relaxation behavior of a quantum dissipative system from the spectral gap of the Liouvillian that governs the time evolution of the density matrix. We investigate the relaxation processes of a quantum dissipative system that exhibits the Liouvillian skin effect, which means that the eigenmodes of the Liouvillian are localized exponentially close to the boundary of the system, and find that the timescale for the system to reach a steady state depends not only on the Liouvillian gap $Δ$ but also on the localization length $ξ$ of the eigenmodes. In particular, we show that the longest relaxation time $τ$ that is maximized over initial states and local observables is given by $τ\sim Δ^{-1}(1+L/ξ)$ with $L$ being the system size. This implies that the longest relaxation time can diverge for $L \to \infty$ without gap closing.
