Liouvillian趋肤效应：弛豫过程的减慢而无间隙闭合
Liouvillian Skin Effect: Slowing Down of Relaxation Processes without Gap Closing
摘要：
从控制密度矩阵时间演化的Liouvillian谱隙中，我们能在多大程度上推断出量子耗散系统的弛豫行为，这是非常重要的。研究了具有Liouvillian趋肤效应的量子耗散系统的弛豫过程，发现系统达到稳态的时间尺度不仅依赖于Liouvillian能隙$Δ$，还依赖于Liouvillian趋肤效应的本征模的局域长度$ξ$.特别是，我们表明，最长的弛豫时间$τ$是最大化的初始状态和局部观测值是由$τ\sim Δ^{-1}(1+L/ξ)$与$L$是系统的大小。这意味着最长的弛豫时间对于$L \to \infty$可以发散而没有间隙闭合。
英文摘要：
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.
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