Path-integral formalism for stochastic resetting: Exactly solved examples and shortcuts to confinement
Abstract
We study the dynamics of overdamped Brownian particles diffusing in conservative force fields and undergoing stochastic resetting to a given location with a generic space-dependent rate of resetting. We present a systematic approach involving path integrals and elements of renewal theory that allows to derive analytical expressions for a variety of statistics of the dynamics such as (i) the propagator prior to first reset; (ii) the distribution of the first-reset time, and (iii) the spatial distribution of the particle at long times. We apply our approach to several representative and hitherto unexplored examples of resetting dynamics. A particularly interesting example for which we find analytical expressions for the statistics of resetting is that of a Brownian particle trapped in a harmonic potential with a rate of resetting that depends on the instantaneous energy of the particle. We find that using energy-dependent resetting processes is more effective in achieving spatial confinement of Brownian particles on a faster timescale than by performing quenches of parameters of the harmonic potential.
Cite
@article{arxiv.1703.10615,
title = {Path-integral formalism for stochastic resetting: Exactly solved examples and shortcuts to confinement},
author = {Édgar Roldán and Shamik Gupta},
journal= {arXiv preprint arXiv:1703.10615},
year = {2017}
}
Comments
v2: Paper expanded to include new results on shortcuts to confinement, title modified, accepted for publication in Phys. Rev. E (2017)