Stochastic resetting of a population of random walks with resetting-rate-dependent diffusivity
arXiv:2205.00817 · doi:10.1088/1751-8121/ac8845
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.
arXiv comment12 pages, submitted to special issue of J. Phys. A on "Stochastic Resetting: Theory and Applications"
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