Controlling particle currents with evaporation and resetting from an interval

Abstract

We investigate the Brownian diffusion of particles in one spatial dimension and in the presence of finite regions within which particles can either evaporate or be reset to a given location. For open boundary conditions, we highlight the appearance of a Brownian yet non-Gaussian diffusion: at long times, the particle distribution is non-Gaussian but its variance grows linearly in time. Moreover, we show that the effective diffusion coefficient of the particles in such systems is bounded from below by $(1-2/\pi )$ times their bare diffusion coefficient. For periodic boundary conditions, i.e., for diffusion on a ring with resetting, we demonstrate a "gauge invariance" of the spatial particle distribution for different choices of the resetting probability currents, in both stationary and non-stationary regimes. Finally, we apply our findings to a stochastic biophysical model for the motion of RNA polymerases during transcriptional pauses, deriving analytically the distribution of the length of cleaved RNA transcripts and the efficiency of RNA cleavage in backtrack recovery.

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• Stochastic resetting: A (very) brief review
• The inspection paradox in stochastic resetting
• Stochastic resetting in interacting particle systems: A review
• Diffusion with Local Resetting and Exclusion
• Synchronization in the Kuramoto model in presence of stochastic resetting
• Resetting transition is governed by an interplay between thermal and potential energy
• Ornstein-Uhlenbeck process and generalizations: particle's dynamics under comb constraints and stochastic resetting
• Stochastic dynamics with multiplicative dichotomic noise: heterogeneous telegrapher's equation, anomalous crossovers and resetting
• Expediting Feller process with stochastic resetting
• Effects of mortality on stochastic search processes with resetting
• Biased random walk on random networks in presence of stochastic resetting: Exact results
• Efficiency of a microscopic heat engine subjected to stochastic resetting
• Stationary-state dynamics of interacting phase oscillators in presence of noise and stochastic resetting
• Designing non-equilibrium states of quantum matter through stochastic resetting