Pascal Principle for Diffusion-Controlled Trapping Reactions

TL;DR

This paper proves that, over long times, an immobile target has a higher survival probability than a mobile one in diffusion-controlled trapping reactions across various dimensions and random walk types.

Contribution

It establishes the Pascal principle for diffusion-controlled trapping, showing mobility does not improve survival chances in such reactions.

Findings

Survival probability of a moving particle is less than or equal to that of an immobile one.

The result holds for large times, arbitrary dimensions, and general random walks.

Applicable to both perfect and imperfect trapping reactions.

Abstract

"All misfortune of man comes from the fact that he does not stay peacefully in his room", has once asserted Blaise Pascal. In the present paper we evoke this statement as the "Pascal principle" in regard to the problem of survival of an "A" particle, which performs a lattice random walk in presence of a concentration of randomly moving traps "B", and gets annihilated upon encounters with any of them. We prove here that at sufficiently large times for both perfect and imperfect trapping reactions, for arbitrary spatial dimension "d" and for a rather general class of random walks, the "A" particle survival probability is less than or equal to the survival probability of an immobile target in the presence of randomly moving traps.