非互作用奥恩斯坦-乌伦贝克过程：奇异点、反常弛豫、赝平衡与边界制冷
Non-reciprocally interacting Ornstein-Uhlenbeck processes: Exceptional points, Anomalous relaxation, Pseudo-equilibrium and Boundary refrigeration
- Tata Institute of Fundamental Research（塔塔基础研究所）
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AI总结：
本文研究非互作用奥恩斯坦-乌伦贝克过程，构建相关模型层级，分析其奇异点、反常弛豫、赝平衡等特性，揭示边界制冷效应及热耗散规律。
AI中文摘要：
非互作用在活性系统、生物系统和无序系统中普遍存在，通常会驱动这些系统偏离平衡。本文引入由可调非互作用参数$g$控制的非互作用奥恩斯坦-乌伦贝克（NROU）模型层级。在特殊点$g=g^*$处，漂移矩阵不可对角化，实现不同阶的奇异点（exceptional points, EPs），此时本征值和本征矢量会同时合并。该层级包含非互作用耦合二聚体、其无序对应物，以及一个多体链，该多体链可精确映射到非厄米量子系统领域中典型的Hatano-Nelson模型。对于无序模型，研究表明，无序实现中EP位置$g^*$的分布在纯净系统的EP处呈现出普适的边缘奇异性，且明显非自平均。在所有模型中，发现EP处自相关函数和协方差函数的常规指数弛豫会被一个多项式时间前因子修饰，该前因子的阶数由EP的阶数决定，其详细结构编码了链的空间结构。在完全不对称时，多体链表现出“赝平衡”：尽管存在非零稳态电流，其稳态分布仍可分解为类似平衡态的单粒子测度；此外，$N$粒子相互作用系统可分解为$N/2$个独立的复OU过程。最后，利用Harada-Sasa关系，得到了总稳态热耗散的闭式表达式，并揭示了一种边界制冷效应，即随着非互作用的调整，边界粒子会从充当热库转变为冷库。
英文摘要：
Non-reciprocal interactions are ubiquitous in active, biological, and disordered systems, generically driving them out of equilibrium. Here, we introduce a hierarchy of non-reciprocally interacting Ornstein-Uhlenbeck (NROU) models governed by a tunable non-reciprocity parameter $g$. At a special point $g=g^*$, the drift matrix becomes non-diagonalizable, realizing exceptional points (EP's) of different orders, where eigenvalues and eigenvectors simultaneously coalesce. The hierarchy encompasses non-reciprocally coupled dimers, their disordered counterparts, and a many-body chain exactly mapping onto the paradigmatic Hatano-Nelson model in the arena of non-Hermitian quantum systems. For the disordered model, we show that the distribution of the EP location $g^*$ across disorder realizations develops a universal edge singularity precisely at the clean-system EP, and is manifestly non-self-averaging. Across all models, we find that at the EP, the usual exponential relaxation of the autocorrelation and covariance functions is dressed by a polynomial-in-time prefactor whose degree is set by the order of the EP and whose detailed structure encodes the spatial architecture of the chain. At complete asymmetry, the many-body chain exhibits ``pseudo-equilibrium'': its steady-state distribution factorizes into equilibrium-like single-particle measures despite a nonzero steady-state current. Moreover, the $N$-particle interacting system decomposes into $N/2$ independent complex OU processes. Finally, using the Harada-Sasa relation, we obtain a closed-form expression for the total steady-state heat dissipation and uncover a boundary refrigeration effect, in which the boundary particles switch from acting as a hot to a cold reservoir as the non-reciprocity is tuned.
