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arXiv 2604.04595cond-mat.stat-mech
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受限环境中自驱动粒子的半马尔可夫动力学:大偏差研究

Semi-Markovian Dynamics of a Self-Propelled Particle in a Confined Environment: A Large-Deviation Study

Faculty of Science, Bu-Ali Sina University(巴阿利·西纳大学理学院)

Shabnam Sohrabi, Farhad H. Jafarpour

AI总结:

通过半马尔可夫过程建模自驱动粒子在受限环境中的运动,研究时间积分电流的大偏差,并发现动力学相变依赖于老化强度。

摘要:

我们研究了在受限环境中移动的自驱动粒子的时间积分电流的大偏差。动力学被建模为半马尔可夫过程,其中在 extit{正常运动阶段}(阶段$0$)和 extit{壁附着阶段}(阶段$1$)之间的转移由时间依赖的重置概率控制。我们研究了两个不同的例子:在第一种情况下,粒子在阶段$0$中进行有偏随机游走,同时间歇性地重置并与容器边界相互作用,在阶段$1$中保持静止。在这种情况下,两个阶段之间转移的重置概率遵循“老化”逻辑。在第二种情况下,粒子在两个活跃阶段之间交替:一个具有无记忆、下游偏置运动的马尔可夫阶段$0$,和一个具有反向上游偏置(代表边界附着导航)的半马尔可夫阶段$1$。这里,我们假设阶段$0$中时间无关的生存概率和阶段$1$中时间依赖的生存概率。通过分析长时间极限下的标度累积量生成函数(SCGF),我们推导出粒子速度涨落中动力学相变(DPT)的条件。我们证明,根据老化强度,系统表现出不连续(一阶)或连续(二阶)的DPT。通过计算机模拟验证了分析预测。

英文摘要:

We study the large deviations of the time-integrated current for a self-propelled particle moving within a confined environment. The dynamics is modeled as a semi-Markovian process, where the transitions between a \textit{normal running phase} (Phase $0$) and a \textit{wall-attached phase} (Phase $1$) are governed by time-dependent reset probabilities. We study two different examples: In the first case, the particle undergoes a biased random walk in Phase $0$, while it intermittently resets and interacts with the container boundaries, remaining stationary in Phase $1$. In this scenario, the reset probabilities for transitions between the two phases follow an ``aging'' logic. In the second case, the particle alternates between two active phases: a Markovian Phase $0$ characterized by memoryless, downstream-biased motion, and a semi-Markovian Phase $1$ with a reversed, upstream bias representing boundary-attached navigation. Here, we assume a time-independent survival probability in Phase $0$ and a time-dependent one in Phase $1$. By analyzing the Scaled Cumulant Generating Function (SCGF) in the long-time limit, we derive the conditions for Dynamical Phase Transition (DPT)s in the fluctuations of the particle velocity. We demonstrate that, depending on the aging strength, the system exhibits either discontinuous (first-order) or continuous (second-order) DPTs. Analytical predictions are validated via computer simulations.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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