论文标题
超出非铁皮皮肤效应以外的耗散晶格模型中的较大松弛时间
Anomalously large relaxation times in dissipative lattice models beyond the non-Hermitian skin effect
论文作者
论文摘要
我们为通用的量子非高铁紧密结合模型展示，局部可观察物的放松时间尺度不受与非富裕皮肤效应相关的本地化长度$ξ_ {\ rm loc} $控制的控制。取而代之的是，特征向量之间的干扰有效地使模式的极端定位与放松无关。这最终是因果关系的结果。着眼于范式的Hatano-Nelson模型，我们证明存在更大的长度尺度$ξ_ {\ rm Prop} $，该$控制着稳定状态的衰减速率。此外，改变$ξ_ {\ rm prop} $可能会导致异常的大放松时间，该松弛时间以系统大小的规模，或者耗散差距正确预测衰减速率的预期行为。我们的工作突出了非铁皮皮肤效应的一个重要方面：这里对边界条件的异常敏感性必然需要有限的时间来表现出来。
We show for generic quantum non-Hermitian tight-binding models that relaxation timescales of local observables are not controlled by the localization length $ξ_{\rm loc}$ associated with the non-Hermitian skin effect, contrary to popular belief. Instead, interference between eigenvectors effectively makes the extreme localization of modes largely irrelevant to relaxation; this is ultimately a consequence of causality and locality. Focusing on the paradigmatic Hatano-Nelson model, we demonstrate that there exists instead a much larger length scale $ξ_{\rm prop}$ which controls the rate of decay towards the steady state. Further, varying $ξ_{\rm prop}$ can lead to anomalously large relaxation times that scale with system size, or to the expected behavior where the dissipative gap correctly predicts the rate of decay. Our work highlights an important aspect of the non-Hermitian skin effect: the exceptional sensitivity to boundary conditions here necessarily takes a finite amount of time to manifest itself.
