The target problem with evanescent subdiffusive traps

TL;DR

This paper investigates how the survival probability of a stationary target is affected by traps that are diffusive or subdiffusive, especially when traps vanish over time, revealing conditions for potential eternal survival.

Contribution

It introduces a model for target survival with evanescent traps and analyzes how trap disappearance influences long-term survival probabilities.

Findings

Trap evanescence can lead to a finite survival probability.

Survival probability depends on the trap disappearance rate.

Constant trap density results in zero survival probability.

Abstract

We calculate the survival probability of a stationary target in one dimension surrounded by diffusive or subdiffusive traps of time-dependent density. The survival probability of a target in the presence of traps of constant density is known to go to zero as a stretched exponential whose specific power is determined by the exponent that characterizes the motion of the traps. A density of traps that grows in time always leads to an asymptotically vanishing survival probability. Trap evanescence leads to a survival probability of the target that may be go to zero or to a finite value indicating a probability of eternal survival, depending on the way in which the traps disappear with time.