标题： 对称简单排斥过程（ASEP）的谱边界——自由费米子、贝特假设和随机矩阵理论 显示英文标题

标题： The spectral boundary of the Asymmetric Simple Exclusion Process (ASEP) -- free fermions, Bethe ansatz and random matrix theory

摘要： 在非平衡统计力学中，不对称简单排斥过程（ASEP）作为一个典型的例子。 我们研究ASEP的谱特性，重点关注其生成矩阵的谱边界。 我们在周期性边界条件（pbc）和开放边界条件（obc）下，考察长度为$L$的有限ASEP链。 值得注意的是，谱边界在pbc下表现出$L$个尖峰，在obc下表现出$L+1$个尖峰。 将ASEP生成矩阵视为一种相互作用的非厄米费米子模型，我们扩展该模型以具有可调相互作用。 在无相互作用的情况下，计算得到的多体谱显示出具有显著尖峰的谱边界。 对于pbc，我们使用坐标Bethe假设在无相互作用情况与ASEP极限之间进行插值，并表明这些尖峰来源于Bethe根的聚集。 通过将ASEP生成矩阵与具有迹相关性的随机矩阵或等效地与具有不同循环结构的随机图相联系，证明了谱边界中尖峰的鲁棒性，两者都显示出类似的尖峰谱边界。 显示英文摘要

摘要： In non-equilibrium statistical mechanics, the Asymmetric Simple Exclusion Process (ASEP) serves as a paradigmatic example. We investigate the spectral characteristics of the ASEP, focusing on the spectral boundary of its generator matrix. We examine finite ASEP chains of length $L$, under periodic (pbc) and open boundary conditions (obc). Notably, the spectral boundary exhibits $L$ spikes for pbc and $L+1$ spikes for obc. Treating the ASEP generator as an interacting non-Hermitian fermionic model, we extend the model to have tunable interaction. In the non-interacting case, the analytically computed many-body spectrum shows a spectral boundary with prominent spikes. For pbc, we use the coordinate Bethe ansatz to interpolate between the noninteracting case to the ASEP limit, and show that these spikes stem from clustering of Bethe roots. The robustness of the spikes in the spectral boundary is demonstrated by linking the ASEP generator to random matrices with trace correlations or, equivalently, random graphs with distinct cycle structures, both displaying similar spiked spectral boundaries.