发表机构
Tokyo University of Science（东京科学大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究探讨波动环境中过阻尼近似的失效，通过对比欠阻尼与过阻尼朗之万动力学，明确了环境平均与惯性消除的非交换性，建立了过阻尼动力学有效性的时间依赖准则。
AI 中文摘要
过阻尼近似被广泛用于描述复杂环境中的布朗运动，但当摩擦系数随时间波动时，其有效性变得不确定。我们通过比较受相同波动摩擦且在相同温度下满足涨落-耗散关系的欠阻尼和过阻尼朗之万动力学来研究这一问题。结果表明，当环境波动相对于速度弛豫较快时，环境平均和惯性消除通常会导致不同的长时间输运。对于快速波动的摩擦，欠阻尼动力学由算术平均摩擦主导，给出有效扩散系数$D_{\rm eff}^{\rm under}=k_{\rm B}T/\langle\gamma\rangle$，而过阻尼动力学给出$D_{\rm eff}^{\rm over}=k_{\rm B}T\langle\gamma^{-1}\rangle$。针对两态马尔可夫摩擦，我们精确推导了有限时间有效扩散系数，并确定了由速度弛豫与环境切换竞争控制的两种 regime 间的完整交叉。我们进一步为一般平稳摩擦过程建立了快速波动结果，并对连续对数-奥恩斯坦-乌伦贝克环境验证了该结果，还可独立确定其特征交叉时间。我们的结果揭示了环境平均与惯性消除间的非交换性，建立了时间依赖的、用于判断 temporally 非均匀环境中过阻尼动力学有效性的准则，并表明快速环境波动可增强而非抑制惯性的影响。
英文摘要
The overdamped approximation is widely used to describe Brownian motion in complex environments, but its validity becomes nontrivial when the friction coefficient itself fluctuates in time. We investigate this problem by comparing underdamped and overdamped Langevin dynamics subject to the same fluctuating friction and satisfying the fluctuation--dissipation relation at a common temperature. We show that environmental averaging and inertial elimination generally lead to different long-time transport when environmental fluctuations are fast compared with velocity relaxation. For rapidly fluctuating friction, the underdamped dynamics is governed by the arithmetic mean friction and yields $D_{\rm eff}^{\rm under}=k_{\rm B}T/\langleγ\rangle$, whereas the overdamped dynamics gives $D_{\rm eff}^{\rm over}=k_{\rm B}T\langleγ^{-1}\rangle$. For a two-state Markov friction, we derive the finite-time effective diffusion coefficient exactly and identify the full crossover between these two regimes, controlled by the competition between velocity relaxation and environmental switching. We further establish the fast-fluctuation result for general stationary friction processes and verify it for a continuous log-Ornstein--Uhlenbeck environment, for which the characteristic crossover time can also be determined independently. Our results reveal a noncommutativity between environmental averaging and inertial elimination, establish a timescale-dependent criterion for the validity of overdamped dynamics in temporally heterogeneous environments, and show that rapid environmental fluctuations can enhance, rather than suppress, the consequences of inertia.
Comments15 pages, 3 figures
