Trapping reactions with subdiffusive traps and particles characterized by different anomalous diffusion exponents

TL;DR

This paper investigates the reaction dynamics of a diffusive particle amidst subdiffusive traps with different anomalous exponents, providing rigorous asymptotic survival probabilities and highlighting cases where existing principles do not apply.

Contribution

It extends the understanding of reaction kinetics to systems with species characterized by different anomalous diffusion exponents, beyond the previously studied identical exponents.

Findings

Derived rigorous asymptotic survival probabilities for most cases.

Identified a special case where normal diffusion coexists with traps having exponents less than 2/3.

Highlighted limitations of the subordination principle in certain anomalous diffusion scenarios.

Abstract

A number of results for reactions involving subdiffusive species all with the same anomalous exponent gamma have recently appeared in the literature and can often be understood in terms of a subordination principle whereby time t in ordinary diffusion is replaced by t^gamma. However, very few results are known for reactions involving different species 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. We find rigorous results for the asymptotic survival probability of the particle in most cases, with the exception of the case of a particle that diffuses normally while the anomalous diffusion exponent of the traps is smaller than 2/3.