Shear-driven diffusion with stochastic resetting

doi:10.1063/5.0243369

Shear-driven diffusion with stochastic resetting

2024-11-13

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I

Iman Abdoli *

K

Kristian Stølevik Olsen

H

Hartmut Löwen

DOI：10.1063/5.0243369

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External flows, such as shear flow, add directional biases to particle motion, introducing anisotropic behavior into the system. Here, we explore the non-equilibrium dynamics that emerge from the interplay between linear shear flow and stochastic resetting. The particle diffuses with a constant diffusion coefficient while simultaneously experiencing linear shear and being stochastically returned to its initial position at a constant rate. We perturbatively derive the steady-state probability distribution that captures the effects of shear-induced anisotropy on the spatial structure of the distribution. We show that the dynamics, which initially spread diffusively, will at late times reach a steady state due to resetting. At intermediate timescales, the system approaches this steady state either by passing through a superdiffusive regime (in the shear-dominated case) or by exhibiting purely sub-diffusive behavior (in the resetting-dominated case). The steady state also gains cross correlations, a feature absent in simpler resetting systems. We also show that the skewness has a non-monotonic behavior when one passes from the shear-dominated to the resetting-dominated regime. We demonstrate that at small resetting rates, the energetic cost of maintaining the steady state becomes significantly higher due to the displacement caused by shear, a unique scaling not seen without shear. Surprisingly, if only the x-position is reset, the system can maintain a Brownian yet non-Gaussian diffusion pattern with non-trivial tails in the distribution.

Keywords:

BROWNIAN-MOTION

SELF-DIFFUSION

PARTICLES

DISPERSION

TIME

FLOW

Shear-driven diffusion with stochastic resetting

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