有效质量方法研究短记忆非马尔可夫系统的动力学
Effective Mass Approach to Dynamics of Non-Markovian Systems with Short Memory
浏览论文内容
中文总结 AI 辅助
本论文提出有效质量方法，将短记忆非马尔可夫系统近似为马尔可夫系统，证明短记忆可显著影响动力学，如反转布朗粒子输运方向，并可用于生成随机信息比特。
中文摘要 AI 辅助
记忆是物理系统动力学的一个固有特征。当系统复杂结构在建模过程中被简化，掩盖了其部分潜在行为时，记忆通常会显现出来。因此，对此类物理模型的正确描述不仅需要了解其当前状态，还需要了解其过去状态，从而导致非马尔可夫动力学。然而，依赖于系统历史的相互作用引入了显著的数学复杂性。为此，当记忆时间远短于表征动力学的时间尺度时，通常以丢失其在系统行为中作用的信息为代价而忽略记忆。在本论文中，我提出了一种新方法，即有效质量方法，它桥接了马尔可夫与非马尔可夫区域，并为分析短记忆系统提供了一个易于处理的框架。在该方法中，非马尔可夫系统被近似为其马尔可夫对应系统，其中短记忆效应被封装在一个有效质量中。随后，我利用该方法证明短记忆对物理动力学的影响可能非常显著。特别地，我展示了在具有时间相关性的环境中布朗粒子的定向输运相对于无记忆介质中的行为可以被反转。此外，我提出了一种设置，其中记忆作为生成随机信息比特的控制参数。总的来说，本论文的结果强调了微观系统中短时间相关性的关键重要性。
英文摘要
Memory is an inherent feature of the dynamics of physical systems. It typically emerges when the complex structure of the system is simplified during the modeling process, obscuring a part of its underlying behavior. Consequently, the correct description of such a physical model requires knowledge of not only its present, but also its past states, leading to non-Markovian dynamics. The resulting interactions depending on the system history, however, introduce a significant layer of mathematical complexity. For this reason, when the memory time is significantly shorter than the time scales characterizing the dynamics, it is typically neglected at the cost of losing information regarding its role in the system behavior. In this dissertation, I introduce a novel methodology, namely the effective mass approach, which bridges the Markovian and non-Markovian regimes and provides an accessible framework for analyzing systems with short memory. In this method, the non-Markovian system is approximated with its Markovian counterpart, in which the short-memory effects are encapsulated within an effective mass. I then utilize this approach to demonstrate that the impact of short memory on physical dynamics can be remarkably pronounced. In particular, I show that the directed transport of a Brownian particle in an environment exhibiting temporal correlations can be reversed relative to its behavior in a memoryless medium. Moreover, I propose a setup wherein memory serves as a~control parameter for the generation of random information bits. Collectively, the results of this dissertation underscore the critical importance of short-time correlations in microscopic systems.
