Mondal Shrabani, Bag Bidhan Chandra
Jadavpur University, Department of Chemistry, Physical Chemistry Section, Kolkata-700032, India.
Visva-Bharati, Department of Chemistry, Santiniketan-731235, India.
Phys Rev E. 2025 Aug;112(2-1):024121. doi: 10.1103/nhmm-dd4l.
In this study, we generalize the theory of stochastic resetting for the non-Markovian dynamics of a free Brownian particle (BP) with arbitrary damping strength and correlation time of the thermal noise. To apply this theory, we calculate the properties of the BP under thermal Ornstein-Uhlenbeck noise and compare the results with those from the Markovian dynamics case. We find that, at long times, the evolution of the distribution function toward the steady state in non-Markovian dynamics can resemble that observed in Markovian systems. In the asymptotic limit, the stationary distribution function reveals that the probability density at a given position can increase exponentially with memory time. Notably, the difference in probability density between the two cases tends to be maximal at an intermediate stage of the dynamics for a fixed memory time. Using the exact distribution function, we also calculate the variance of the position to explore a central question: How the nature of diffusion for a free particle is influenced by resetting, which can lead to a steady state. This analysis suggests that, although ballistic diffusion and memory effects may not significantly impact the long-time behavior of free Brownian motion or equilibrium in the presence of an external conservative force field, they play a crucial role in the formation of a resetting-induced localized stationary state. Additionally, we observe that the survival probability decreases exponentially at all times. Finally, we compute the mean first-passage time and uncover interesting results that provide further insights into the system's behavior.
在本研究中，我们推广了随机重置理论，用于具有任意阻尼强度和热噪声关联时间的自由布朗粒子（BP）的非马尔可夫动力学。为应用该理论，我们计算了热奥恩斯坦 - 乌伦贝克噪声下BP的性质，并将结果与马尔可夫动力学情况的结果进行比较。我们发现，在长时间情况下，非马尔可夫动力学中分布函数向稳态的演化可能类似于马尔可夫系统中观察到的情况。在渐近极限中，稳态分布函数表明给定位置处的概率密度可以随记忆时间呈指数增加。值得注意的是，对于固定的记忆时间，两种情况之间的概率密度差异在动力学的中间阶段往往最大。使用精确的分布函数，我们还计算了位置的方差，以探讨一个核心问题：重置如何影响自由粒子的扩散性质，这可能导致一个稳态。该分析表明，尽管弹道扩散和记忆效应在存在外部保守力场时可能不会对自由布朗运动的长期行为或平衡产生显著影响，但它们在重置诱导的局部稳态的形成中起着关键作用。此外，我们观察到生存概率在所有时间都呈指数下降。最后，我们计算了平均首次通过时间，并发现了有趣的结果，这些结果为系统行为提供了进一步的见解。
