Stochastic resetting in underdamped Brownian motion

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.

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• Stochastic resetting and first arrival subjected to Gaussian noise and Poisson white noise
• The one-dimensional telegraphic process with noninstantaneous stochastic resetting
• Winding number of a Brownian particle on a ring under stochastic resetting
• Inducing and optimizing Markovian Mpemba effect with stochastic reset