AI 中文总结
研究具有单格点损耗的开放SSH链，通过多体费米子林德布拉德问题简化为有限非厄米单体矩阵，揭示拓扑、缺陷几何和局部耗散共同组织长时间弛豫的三种机制及不同损耗下的动力学特征。
AI 中文摘要
我们研究了具有单格点损耗的二次开放SSH链，表明多体费米子林德布拉德问题可精确简化为具有一阶虚杂质的有限非厄米单体矩阵。其快度生成完整的刘维尔谱，并揭示了三种控制最慢弛豫的机制。在弱损耗时，损耗格点处的干净局部谱权重决定衰减，产生一般规律$\Delta_{\mathcal L}\sim\gamma N^{-3}$，在拓扑区域，边缘控制的能隙呈指数级更小。在中等损耗时，中心体损耗几何结构在实$\gamma$轴上达到精确的例外点。与对称性相关的快度对同时合并，包括较低快度边缘处的对。在这个较低边缘例外点处的精确实空间动力学表现出多项式增强的指数尾部，而具有相同奇偶性偶数单体衰减边缘但无较低边缘缺陷的匹配高能控制仍接近指数形式。在强损耗时，一个超快缺陷模式与由截断链芝诺问题控制的活跃慢扇区分离，给出$\Delta_{\mathcal L}\sim\gamma^{-1}$，直至与几何相关的前置因子。完整的有限费米子刘维尔谱，包括其算符奇偶性扇区和子集和结构，是特定于统计的。相比之下，基本的单体衰减谱和三种相关机制由有限维线性漂移矩阵控制，因此它们的谱和动力学特征也可以在设计用于实现相同有效矩阵的玻色子和经典波平台中获得。这些结果确定了拓扑、缺陷几何和局部耗散如何共同组织开放二聚化晶格中的长时间弛豫。
英文摘要
We study a quadratic open SSH chain with a single-site loss and show that the many-body fermionic Lindblad problem admits an exact reduction to a finite non-Hermitian one-body matrix with a rank-one imaginary impurity. Its rapidities generate the complete Liouvillian spectrum and reveal three mechanisms governing the slowest relaxation. At weak loss, decay is selected by the clean local spectral weight at the lossy site, yielding the generic law $Δ_{\mathcal L}\simγN^{-3}$ and, in the topological regime, exponentially smaller edge-controlled gaps. At intermediate loss, a centered bulk-loss geometry reaches an exact exceptional point on the real-$γ$ axis. Symmetry-related rapidity pairs coalesce simultaneously, including the pair at the lower rapidity edge. Exact real-space dynamics at this lower-edge exceptional point exhibits a polynomially enhanced exponential tail, whereas a matched high-energy control with the same parity-even one-body decay edge but no lower-edge defectiveness remains nearly exponential. At strong loss, one ultrafast defect mode separates from an active slow sector governed by a cut-chain Zeno problem, giving $Δ_{\mathcal L}\simγ^{-1}$ up to a geometry-dependent prefactor. The full finite fermionic Liouvillian spectrum, including its operator-parity sectors and subset-sum structure, is statistics-specific. By contrast, the elementary one-body decay spectrum and the three associated mechanisms are governed by a finite-dimensional linear drift matrix, so their spectral and dynamical signatures can also be accessed in bosonic and classical-wave platforms engineered to realize the same effective matrix. These results establish how topology, defect geometry, and local dissipation jointly organize long-time relaxation in an open dimerized lattice.
Comments23 pages, 5 figures (accepted by Physical Review A)
