Di Bello Costantino, Hartmann Alexander K, Majumdar Satya N, Mori Francesco, Rosso Alberto, Schehr Grégory
Institute for Physics & Astronomy, University of Potsdam, 14476 Potsdam-Golm, Germany.
Institut für Physik, Universität Oldenburg, Oldenburg, Germany.
Phys Rev E. 2023 Jul;108(1-1):014112. doi: 10.1103/PhysRevE.108.014112.
We consider a system of noninteracting particles on a line with initial positions distributed uniformly with density ρ on the negative half-line. We consider two different models: (i) Each particle performs independent Brownian motion with stochastic resetting to its initial position with rate r and (ii) each particle performs run-and-tumble motion, and with rate r its position gets reset to its initial value and simultaneously its velocity gets randomized. We study the effects of resetting on the distribution P(Q,t) of the integrated particle current Q up to time t through the origin (from left to right). We study both the annealed and the quenched current distributions and in both cases, we find that resetting induces a stationary limiting distribution of the current at long times. However, we show that the approach to the stationary state of the current distribution in the annealed and the quenched cases are drastically different for both models. In the annealed case, the whole distribution P_{an}(Q,t) approaches its stationary limit uniformly for all Q. In contrast, the quenched distribution P_{qu}(Q,t) attains its stationary form for Q<Q_{crit}(t), while it remains time dependent for Q>Q_{crit}(t). We show that Q_{crit}(t) increases linearly with t for large t. On the scale where Q∼Q_{crit}(t), we show that P_{qu}(Q,t) has an unusual large deviation form with a rate function that has a third-order phase transition at the critical point. We have computed the associated rate functions analytically for both models. Using an importance sampling method that allows to probe probabilities as tiny as 10^{-14000}, we were able to compute numerically this nonanalytic rate function for the resetting Brownian dynamics and found excellent agreement with our analytical prediction.
我们考虑一个粒子在直线上的非相互作用系统，其初始位置在负半轴上以密度ρ均匀分布。我们考虑两种不同的模型：（i）每个粒子进行独立的布朗运动，并以速率r随机重置到其初始位置；（ii）每个粒子进行奔跑-翻滚运动，并且以速率r其位置被重置到初始值，同时其速度被随机化。我们研究重置对直到时间t通过原点（从左到右）的积分粒子电流Q的分布P(Q,t)的影响。我们研究了退火电流分布和淬火电流分布，并且在这两种情况下，我们发现重置在长时间诱导了电流的一个平稳极限分布。然而，我们表明，对于这两种模型，退火情况和淬火情况中电流分布到平稳状态的方法有很大不同。在退火情况下，对于所有的Q，整个分布P_{an}(Q,t)均匀地接近其平稳极限。相反，淬火分布P_{qu}(Q,t)对于Q<Q_{crit}(t)达到其平稳形式，而对于Q>Q_{crit}(t)它仍然依赖于时间。我们表明，对于大的t，Q_{crit}(t)随t线性增加。在Q∼Q_{crit}(t)的尺度上，我们表明P_{qu}(Q,t)具有一种不寻常的大偏差形式，其速率函数在临界点处有一个三阶相变。我们已经对这两种模型解析地计算了相关的速率函数。使用一种重要性采样方法，该方法允许探测低至10^{-14000}的概率，我们能够对重置布朗动力学数值计算这个非解析速率函数，并发现与我们的解析预测有很好的一致性。
