标题： 微尺度和纳米尺度系统在弱记忆效应区域的动力学 显示英文标题

标题： Dynamics of Micro and Nanoscale Systems in the Weak-Memory Regime

摘要： 记忆效应在小尺度系统中普遍存在。 它们来源于可访问和不可访问自由度之间的相互作用，并导致时间非局部的演化方程。 如果可访问和不可访问自由度的特征时间尺度明显分离，可以通过标准马尔可夫近似恢复局部性。 在这里，我们表明这种方法可以严格扩展到一个定义明确的弱记忆区域，在该区域内相关的时间尺度可以具有可比较的数量级。 我们推导了局部近似误差的显式界限，并为其构建提供了一个收敛的微扰方案。 适用于任何与感兴趣的变量呈线性且自主的非局部时间演化方程，我们的理论为记忆效应的系统描述提供了统一的框架。 显示英文摘要

摘要： Memory effects are ubiquitous in small-scale systems. They emerge from interactions between accessible and inaccessible degrees of freedom and give rise to evolution equations that are non-local in time. If the characteristic time scales of accessible and inaccessible degrees of freedom are sharply separated, locality can be restored through the standard Markov approximation. Here, we show that this approach can be rigorously extended to a well-defined weak-memory regime, where the relevant time scales can be of comparable order of magnitude. We derive explicit bounds on the error of the local approximation and a convergent perturbation scheme for its construction. Being applicable to any non-local time evolution equation that is autonomous and linear in the variables of interest, our theory provides a unifying framework for the systematic description of memory effects.