Resetting by rescaling: Exact results for a diffusing particle in one dimension.

IF 2.2 3区物理与天体物理 Q2 PHYSICS, FLUIDS & PLASMAS

Physical Review E Pub Date : 2024-10-01 DOI:10.1103/PhysRevE.110.044142

Marco Biroli, Yannick Feld, Alexander K Hartmann, Satya N Majumdar, Grégory Schehr

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Abstract

In this paper, we study a simple model of a diffusive particle on a line, undergoing a stochastic resetting with rate r, via rescaling its current position by a factor a, which can be either positive or negative. For |a|<1, the position distribution becomes stationary at long times and we compute this limiting distribution exactly for all |a|<1. This symmetric distribution has a Gaussian shape near its peak at x=0, but decays exponentially for large |x|. We also studied the mean first-passage time (MFPT) T(0) to a target located at a distance L from the initial position (the origin) of the particle. As a function of the initial position x, the MFPT T(x) satisfies a nonlocal second order differential equation and we have solved it explicitly for 0≤a<1. For -1

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通过重新缩放进行重置：一维扩散粒子的精确结果

在本文中，我们研究了一个简单的模型，即直线上的一个扩散粒子，通过用系数 a（可以是正值或负值）重置其当前位置，以速率 r 进行随机重置。对于 |a

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Physical Review E PHYSICS, FLUIDS & PLASMASPHYSICS, MATHEMAT-PHYSICS, MATHEMATICAL

CiteScore

4.50

自引率

16.70%

发文量

2110

期刊介绍： Physical Review E (PRE), broad and interdisciplinary in scope, focuses on collective phenomena of many-body systems, with statistical physics and nonlinear dynamics as the central themes of the journal. Physical Review E publishes recent developments in biological and soft matter physics including granular materials, colloids, complex fluids, liquid crystals, and polymers. The journal covers fluid dynamics and plasma physics and includes sections on computational and interdisciplinary physics, for example, complex networks.