Survival Probability of a Mobile Particle in a Fluctuating Field

TL;DR

This paper investigates the survival probability of a mobile particle in fluctuating fields, analyzing different particle motions and external field types, and calculating the decay exponent through various methods.

Contribution

It introduces a comprehensive study of mobile particle survival in dynamic fields, extending static persistence concepts to moving particles with new analytical and numerical results.

Findings

Survival probability decays as a power law with exponent θ_m.

Different external fields influence the decay behavior.

Analytical and numerical methods yield consistent estimates of θ_m.

Abstract

We study the the survival probability P(t) upto time t, of a test particle moving in a fluctuating external field. The particle moves according to some prescribed deterministic or stochastic rules and survives as long as the external field that it sees at its own location does not change sign. This is a natural generalization of the "static persistence" (when the particle is at rest) that has generated considerable recent interests. Two types of motions of the particle are considered. In one case, the particle adopts a strategy to live longer and in the other it just diffuses randomly. Three different external fields were considered: (i) the solution of diffusion equation, (ii) the "colour" profile of the q-state Potts model undergoing zero temperature coarsening dynamics and (iii) spatially uncorrelated Brownian signals. In most cases studied, $P(t)\sim t^{-\theta_m}$ for large t. The exponent $\theta_m$ is calculated via numerically, analytically by approximate methods and in some cases exactly. It is shown in some special cases that the survival probability of the mobile particle is related to the persistence of special "patterns" present in the initial configuration of a phase ordering system.