Stochastic resetting of a population of random walks with resetting-rate-dependent diffusivity

Abstract

We consider the problem of diffusion with stochastic resetting in a population of random walks where the diffusion coefficient is not constant, but behaves as a power-law of the average resetting rate of the population. Resetting occurs only beyond a threshold distance from the origin. This problem is motivated by physical realizations like soft matter under shear, where diffusion of a walk is induced by resetting events of other walks. We first reformulate in the broader context of diffusion with stochastic resetting the so-called Hébraud-Lequeux model for plasticity in dense soft matter, in which diffusivity is proportional to the average resetting rate. Depending on parameter values, the response to a weak external field may be either linear or non-linear with a non-zero average position for a vanishing applied field, and the transition between these two regimes may be interpreted as a continuous phase transition. Extending the model by considering a general power-law relation between diffusivity and average resetting rate, we notably find a discontinuous phase transition between a finite diffusivity and a vanishing diffusivity in the small field limit.

12 pages, submitted to special issue of J. Phys. A on "Stochastic Resetting: Theory and Applications"

References in corpus (11)

• First order transition for the optimal search time of Lévy flights with resetting
• Diffusion with resetting in arbitrary spatial dimension
• Monotonous continuous-time random walks with drift and stochastic reset events
• Optimization in First-Passage Resetting
• Stochastic resetting in underdamped Brownian motion
• On the relevance of disorder in athermal amorphous materials under shear
• Record statistics for random walks and Lévy flights with resetting
• Optimization and Growth in First-Passage Resetting
• Maximum and records of random walks with stochastic resetting
• Theoretical approaches to the steady-state statistical physics of interacting dissipative units
• Effect of tax dynamics on linearly growing processes under stochastic resetting: a possible economic model

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