论文标题
liouvillian皮肤效应在可解决的模型中
Liouvillian Skin Effect in an Exactly Solvable Model
论文作者
论文摘要
耗散，拓扑和对边界条件的敏感性之间的相互作用最近吸引了有效的非弱点描述水平的大量关注。在这里，我们精确地解决了一个量子机械林布拉德主方程，描述了开放边界条件（OBC）和周期性边界条件（PBC）的耗散拓扑su-schrieffer-heeger（SSH）链（SSH）链。我们发现，对与非铁皮皮肤效应相关的边界条件的极端敏感性直接反映在管理密度矩阵的时间演化的速度中，从而引起了liouvillian皮肤效应。这导致了几种有趣的现象，包括边界敏感的阻尼行为，有限周期系统中的稳态电流以及在大型系统极限的放松时间分化。我们阐明了这些系统中拓扑的作用在有效的非热汉密尔顿限制和完整的主方程框架中如何有所不同。
The interplay between dissipation, topology and sensitivity to boundary conditions has recently attracted tremendous amounts of attention at the level of effective non-Hermitian descriptions. Here we exactly solve a quantum mechanical Lindblad master equation describing a dissipative topological Su-Schrieffer-Heeger (SSH) chain of fermions for both open boundary condition (OBC) and periodic boundary condition (PBC). We find that the extreme sensitivity on the boundary conditions associated with the non-Hermitian skin effect is directly reflected in the rapidities governing the time evolution of the density matrix giving rise to a Liouvillian skin effect. This leads to several intriguing phenomena including boundary sensitive damping behavior, steady state currents in finite periodic systems, and diverging relaxation times in the limit of large systems. We illuminate how the role of topology in these systems differs in the effective non-Hermitian Hamiltonian limit and the full master equation framework.
