# Stochastic resetting in underdamped Brownian motion

## TL;DR

This paper investigates the effects of stochastic resetting on the position distribution of an underdamped Brownian particle, deriving steady-state and transient behaviors through analytical and numerical methods.

## Contribution

It introduces a model of stochastic resetting in underdamped Brownian motion and analyzes the resulting nonequilibrium steady state and transient dynamics.

## Key findings

- Derived analytical expressions for steady-state position distribution.
- Verified analytical results with numerical simulations.
- Characterized the approach to steady state over time.

## Abstract

We consider a single Brownian particle in one dimension in a medium at a constant temperature in the underdamped regime. We stochastically reset the position of the Brownian particle to a fixed point in the space with a constant rate $r$ whereas its velocity evolves irrespective of the position of the particle and stochastic resetting mechanism. The nonequilibrium steady state of the position distribution is studied for this model system. Further, we study the distribution of the position of the particle in the finite time and the approach to the nonequilibrium steady state distribution with time. Numerical simulations are done to verify the analytical results.