Trapping reactions with subdiffusive traps and particles

TL;DR

This paper investigates the reaction dynamics of subdiffusive particles and traps in one dimension, providing rigorous asymptotic survival probabilities under various conditions, with some cases remaining unresolved.

Contribution

It offers new analytical results for the survival probability of subdiffusive particles amidst traps with different anomalous diffusion exponents, extending understanding of reaction kinetics in anomalous diffusion systems.

Findings

Rigorous asymptotic survival probabilities derived for most cases.

Identified unresolved case where particle diffuses normally and traps have exponent less than 2/3.

Enhanced understanding of reaction dynamics involving subdiffusive species.

Abstract

Reaction dynamics involving subdiffusive species is an interesting topic with only few known results, especially when the motion of different species is characterized by different anomalous diffusion exponents. Here we study the reaction dynamics of a (sub)diffusive particle surrounded by a sea of (sub)diffusive traps in one dimension. Under some reasonable assumptions we find rigorous results for the asymptotic survival probability of the particle in most cases, but have not succeeded in doing so for a particle that diffuses normally while the anomalous diffusion exponent of the traps is smaller than 2/3.