First passage in the presence of stochastic resetting and a potential barrier

TL;DR

This paper investigates how stochastic resetting affects diffusion and first passage times in systems with potential barriers, revealing phase transitions where resetting's advantage disappears, with exact and numerical analyses across different potentials.

Contribution

It provides a systematic analysis of resetting effects in models with potential barriers, identifying conditions for transitions and the impact of potential asymmetry and boundary conditions.

Findings

Exact analytical results for a tent-potential model.

Numerical results for a quartic-potential system.

Identification of parameter regions where resetting loses its advantage.

Abstract

Diffusion and first passage in the presence of stochastic resetting and potential bias have been of recent interest. We study a few models, systematically progressing in their complexity, to understand the usefulness of resetting. In the parameter space of the models, there are multiple continuous and discontinuous transitions where the advantage of resetting vanishes. We show these results analytically exactly for a tent-potential, and numerically accurately for a quartic-potential relevant to a magnetic system at low temperatures. We find that the spatial asymmetry of the potential across the barrier, and the number of absorbing boundaries, play a crucial role in determining the type of transition.