论文标题
随机重置的随机步行人群，依赖于重置率的扩散率
Stochastic resetting of a population of random walks with resetting-rate-dependent diffusivity
论文作者
论文摘要
我们考虑在扩散系数不恒定的随机步行中随机重置扩散的问题，而是表现为人口平均重置率的幂律。重置仅在距离原点的阈值距离之内。这个问题是由诸如剪切中的软物质之类的物理实现的动机，在剪切中，步行的扩散是通过重置其他步行事件引起的。我们首先在扩散的更广泛的背景下，随机重置在致密软物质中的所谓Hébraud-Lequeux模型，其中扩散率与平均重置率成正比。根据参数值，对弱外部场的响应可以是线性的，也可以是非线性的，对于消失的施加场的平均位置非零平均位置，并且这两个方案之间的过渡可以解释为连续相变。通过考虑扩散率和平均重置率之间的一般力量关系来扩展模型，我们发现有限扩散率与小场限制中消失的扩散率之间的不连续相变。
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.
