Stochastic resetting in non-thermal bath:

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We study the dynamics of an overdamped Brownian particle subjected to Poissonian stochastic resetting in a non-thermal bath, characterized by a Poisson white noise and a Gaussian noise. Applying the renewal theory we find an exact analytical expression for the spatial distribution at the steady state. Unlike the single exponential distribution as observed in case of a purely thermal bath, the distribution is double-exponential. Relaxation of the transient spatial distributions to the stationary one, for the limiting cases of Poissonian rate is investigated carefully. In addition, we study the first-arrival properties of the system in the presence of a delta-function sink with strength κ, where κ = 0 and κ = ∞ correspond to fully non-reactive and fully reactive sinks respectively. We explore the effect of two competitive mechanisms - the diffusive spread in the presence of two noises and the increase in probability density around the initial position due to stochastic resetting. We show that there exists an optimal resetting rate, which minimizes the mean first-arrival time (MFAT) to the sink for a given value of the sink strength. We also explore the effect of the strength of the Poissonian noise on MFAT, in addition to sink strength. Our formalism generalizes the diffusion-limited reaction under resetting in a nonequilibrium bath and provides an efficient search strategy for a reactant to find a target site, relevant in a range of biophysical processes.

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Relevant Publication(s):

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1. Stochastic resetting and first arrival subjected to Gaussian noise and Poisson white noise - Koushik Goswami and Rajarshi Chakrabarti, Phys. Rev. E 104, 034113 (2021).

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