发表机构
University of Ljubljana; Laboratoire de Physique de l’École Normale Superieure, CNRS, ENS & Université PSL, Sorbonne Université, Université Paris Cité（卢布尔雅那大学; 巴黎高等师范学院物理实验室，法国国家科学研究中心，巴黎文理研究大学，索邦大学，巴黎西岱大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究针对离散幺正系统，以CMV矩阵为对象，通过正交多项式理论识别出两类弛豫相，明确了RP共振的特性及不同方法的一致性，为幺多体系统动力学提供了精确结果。
AI 中文摘要
截断传播子的主导本征值，即Ruelle-Pollicott（RP）共振，是处理幺正多体系统动力学的一种优雅方法。我们研究了其标准形式为CMV矩阵（数学文献中已知）的幺正传播子，并得到了RP共振及相关范数发散本征向量的若干精确结果。针对由杂质单侧移位构成、受双幺正电路中算子动力学启发的最简CMV类，我们得到了闭式结果，尤其证明了获取RP共振的三种独立方式——截断传播子、预解式的解析延拓以及 rigged Hilbert 空间方法——均给出相同结果。在更贴近实际的CMV矩阵中，混沌系统特有的类移位算子动力学仅为渐近存在，我们借助单位圆上正交多项式的丰富理论识别出两个相。第一相中，弛豫源于局域算子有效演化为非局域性不断增强、回流可忽略的算子；尤其有趣的是第二相，其因大算子回流的贡献而表现出更快的弛豫，且RP共振不等于截断传播子的本征值，而是“隐藏”在一组病态本征值构成的环内。
英文摘要
Leading eigenvalues of the truncated propagator, known as Ruelle-Pollicott (RP) resonances, are an elegant way of addressing the dynamics of unitary many-body systems. We study unitary propagators in their canonical form, known in the mathematical literature as the CMV matrices, and obtain a number of exact results for RP resonances and the associated norm-diverging eigenvectors. For the simplest CMV class describing a unilateral shift with an impurity, motivated by operator dynamics in dual-unitary circuits, we obtain closed-form results and in particular show that the three independent ways of obtaining RP resonances -- the truncated propagator, analytic continuation of the resolvent, and the rigged Hilbert space approach -- all give the same results. In more realistic CMV matrices, in which shift-like operator dynamics characteristic of chaotic systems is only asymptotic, we rely on the rich theory of orthogonal polynomials on the unit circle and identify two phases. In the first phase, relaxation occurs due to local operators effectively evolving into increasingly nonlocal ones with negligible backflow. Especially interesting is the second phase, which, surprisingly, exhibits faster relaxation because of contributions from the backflow of large operators. Additionally, in the second phase, RP resonances are not equal to the eigenvalues of the truncated propagator, instead, they are ``hidden'' within a ring of ill-conditioned eigenvalues.
Comments34 + 12 pages
