投射诱发记忆的表现：一般理论与倾斜的单文件
Manifestations of Projection-Induced Memory: General Theory and the Tilted Single File
摘要：
多年来，非马尔可夫随机过程和反常扩散领域从一个专门的主题发展成为主流理论，它跨越了物理学、化学、生物学和生态学的领域。出现了许多唯象学方法，这些方法或多或少可以成功地再现或解释凝聚态、生物和/或单粒子系统中的实验观察。然而，就他们的预测而言，这些方法并不是唯一的，通常建立在概念上正交的想法，并且通常在特设的基础上使用。因此，从更精细的原则出发，建立一个系统的、数学上统一的和干净的方法似乎是及时和可取的。在这里，我们分析投影诱导遍历非马尔可夫动力学，可逆的以及不可逆的，使用谱理论。我们调查的历史投影和潜在的观测，引起记忆投影动态之间的动态相关性，并严格建立条件下，投影动态是马尔可夫或更新。提出了一种系统的度量方法来量化非马尔可夫性的程度。作为一个简单的，说明性的，但不平凡的例子，我们研究单文件扩散在一个倾斜的盒子，这是第一次，我们完全解决了使用坐标贝特anomaly。我们的结果为更深入、更系统地分析投影诱导的非马尔可夫动力学和反常扩散提供了坚实的基础。
英文摘要：
Over the years the field of non-Markovian stochastic processes and anomalous diffusion evolved from a specialized topic to mainstream theory, which transgressed the realms of physics to chemistry, biology and ecology. Numerous phenomenological approaches emerged, which can more or less successfully reproduce or account for experimental observations in condensed matter, biological and/or single-particle systems. However, as far as their predictions are concerned these approaches are not unique, often build on conceptually orthogonal ideas, and are typically employed on an ad hoc basis. It therefore seems timely and desirable to establish a systematic, mathematically unifying and clean approach starting from more fine-grained principles. Here we analyze projection-induced ergodic non-Markovian dynamics, both reversible as well as irreversible, using spectral theory. We investigate dynamical correlations between histories of projected and latent observables that give rise to memory in projected dynamics, and rigorously establish conditions under which projected dynamics is Markovian or renewal. A systematic metric is proposed for quantifying the degree of non-Markovianity. As a simple, illustrative but non-trivial example we study single file diffusion in a tilted box, which, for the first time, we solve exactly using the coordinate Bethe ansatz. Our results provide a solid foundation for a deeper and more systematic analysis of projection-induced non-Markovian dynamics and anomalous diffusion.
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