Trapping reaction in a symmetric double well potential

TL;DR

This paper investigates the survival probability of particles in a symmetric double well potential with a trap, analyzing the effects of confinement, trapping, and growth, with applications to population dynamics under predation.

Contribution

It provides an analytical solution for survival probability using Green's functions and explores the impact of growth and trapping rates on population extinction.

Findings

Existence of a threshold trapping rate leading to population extinction.

Analytical expression for survival probability in double well potentials.

Numerical simulations confirm theoretical predictions.

Abstract

We study the trapping reaction-diffusion problem in a symmetric double well potential in one dimension with a static trap located at the middle of the central barrier of the double well. The effect of competition between the confinement and the trapping process on the time evolution of the survival probability is considered. The solution for the survival probability of a particle is obtained by the method of Green's function. Furthermore, we study trapping in the presence of a growth term. We show that for a given growth rate there exist a threshold trapping rate beyond which the population can become extinct asymptotically. Numerical simulations for a symmetric quartic potential are done and results are discussed. This model can be applied to study the dynamics of a population in habitats with a localized predation.