Santra Saikat, Singh Prashant
International Centre for Theoretical Sciences, Tata Institute of Fundamental Research, Bengaluru 560089, India.
Niels Bohr International Academy, Niels Bohr Institute, University of Copenhagen, Blegdamsvej 17, 2100 Copenhagen, Denmark.
Phys Rev E. 2024 Mar;109(3-1):034123. doi: 10.1103/PhysRevE.109.034123.
Resetting is a renewal mechanism in which a process is intermittently repeated after a random or fixed time. This simple act of stop and repeat profoundly influences the behavior of a system as exemplified by the emergence of nonequilibrium properties and expedition of search processes. Herein we explore the ramifications of stochastic resetting in the context of a single-file system called random average process (RAP) in one dimension. In particular, we focus on the dynamics of tracer particles and analytically compute the variance, equal time correlation, autocorrelation, and unequal time correlation between the positions of different tracer particles. Our study unveils that resetting gives rise to rather different behaviors depending on whether the particles move symmetrically or asymmetrically. For the asymmetric case, the system for instance exhibits a long-range correlation which is not seen in absence of the resetting. Similarly, in contrast to the reset-free RAP, the variance shows distinct scalings for symmetric and asymmetric cases. While for the symmetric case, it decays (towards its steady value) as ∼e^{-rt}/sqrt[t], we find ∼te^{-rt} decay for the asymmetric case (r being the resetting rate). Finally, we examine the autocorrelation and unequal time correlation in the steady state and demonstrate that they obey interesting scaling forms at late times. All our analytical results are substantiated by extensive numerical simulations.
重置是一种更新机制，其中一个过程在随机或固定时间后会间歇性地重复。这种简单的停止和重复行为会深刻影响系统的行为，例如非平衡性质的出现和搜索过程的加速。在此，我们在一维的称为随机平均过程（RAP）的单文件系统背景下探索随机重置的影响。特别地，我们关注示踪粒子的动力学，并解析计算不同示踪粒子位置之间的方差、等时关联、自关联和不等时关联。我们的研究表明，根据粒子是对称移动还是不对称移动，重置会产生截然不同的行为。例如，对于不对称情况，系统表现出一种在没有重置时看不到的长程关联。同样，与无重置的RAP相比，方差在对称和不对称情况下呈现出不同的标度。对于对称情况，它以 ∼e^{-rt}/sqrt[t] 的形式衰减（趋向于其稳态值），而对于不对称情况，我们发现其衰减形式为 ∼te^{-rt}（r 为重置率）。最后，我们研究了稳态下的自关联和不等时关联，并证明它们在长时间时遵循有趣的标度形式。我们所有的解析结果都通过广泛的数值模拟得到了证实。
