Random acceleration process on finite intervals under stochastic restarting

TL;DR

This paper investigates how stochastic resetting protocols affect the escape dynamics of a randomly accelerated particle within a finite interval, revealing that full resetting can facilitate escape while partial resetting can trap the particle.

Contribution

It compares three resetting protocols for a stochastic acceleration process and analyzes their impact on escape times using the Langevin equation.

Findings

Full resetting can facilitate escape kinetics.

Partial resetting of velocity or position can trap the particle.

Frequent position resetting traps the particle regardless of initial velocity.

Abstract

The escape of the randomly accelerated undamped particle from the finite interval under action of stochastic resetting is studied. The motion of such a particle is described by the full Langevin equation and the particle is characterized by the position and velocity. We compare three resetting protocols, which restarts velocity or position (partial resetting) and the whole motion (position and velocity -- full resetting). Using the mean first passage time we assess efficiency of restarting protocols in facilitating or suppressing the escape kinetics. There are fundamental differences between partial resetting scenarios which restart velocity or position, as in the limit of very frequent resets only the position resetting (regardless of initial velocity) can trap the particle in the finite domain of motion. The velocity resetting or the simultaneous position and velocity restarting provide a possibility of facilitating the undamped escape kinetics.