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arXiv · 1703.10615

Path-integral formalism for stochastic resetting: Exactly solved examples and shortcuts to confinement

Édgar Roldán·Shamik Gupta
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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.

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BibTeXRIS

Édgar Roldán, Shamik Gupta. 2017-07-26. Path-integral formalism for stochastic resetting: Exactly solved examples and shortcuts to confinement. https://doi.org/10.1103/physreve.96.022130

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