Roldán Édgar, Gupta Shamik
Max-Planck Institute for the Physics of Complex Systems, cfAED and GISC, Nöthnitzer Straße 38, 01187 Dresden, Germany.
Department of Physics, Ramakrishna Mission Vivekananda University, Belur Math, Howrah 711 202, West Bengal, India.
Phys Rev E. 2017 Aug;96(2-1):022130. doi: 10.1103/PhysRevE.96.022130. Epub 2017 Aug 14.
We study the dynamics of overdamped Brownian particles diffusing in conservative force fields and undergoing stochastic resetting to a given location at a generic space-dependent rate of resetting. We present a systematic approach involving path integrals and elements of renewal theory that allows us to derive analytical expressions for a variety of statistics of the dynamics such as (i) the propagator prior to first reset, (ii) the distribution of the first-reset time, and (iii) the spatial distribution of the particle at long times. We apply our approach to several representative and hitherto unexplored examples of resetting dynamics. A particularly interesting example for which we find analytical expressions for the statistics of resetting is that of a Brownian particle trapped in a harmonic potential with a rate of resetting that depends on the instantaneous energy of the particle. We find that using energy-dependent resetting processes is more effective in achieving spatial confinement of Brownian particles on a faster time scale than performing quenches of parameters of the harmonic potential.
我们研究了过阻尼布朗粒子在保守力场中扩散，并以一般的空间依赖重置率随机重置到给定位置的动力学。我们提出了一种系统的方法，该方法涉及路径积分和更新理论的元素，使我们能够推导出动力学各种统计量的解析表达式，例如：（i）首次重置前的传播子；（ii）首次重置时间的分布；（iii）长时间后粒子的空间分布。我们将我们的方法应用于几个具有代表性且迄今未探索的重置动力学示例。我们找到重置统计量解析表达式的一个特别有趣的例子是，一个布朗粒子被困在一个谐振子势中，其重置率取决于粒子的瞬时能量。我们发现，与对谐振子势的参数进行猝灭相比，使用能量依赖的重置过程在更快的时间尺度上实现布朗粒子的空间限制更有效。
