Singh R K, Górska K, Sandev T
Department of Physics, Bar-Ilan University, Ramat-Gan 5290002, Israel.
Institute of Nuclear Physics, Polish Academy of Sciences, Radzikowskiego 152, PL-31342 Kraków, Poland.
Phys Rev E. 2022 Jun;105(6-1):064133. doi: 10.1103/PhysRevE.105.064133.
We address the effect of stochastic resetting on diffusion and subdiffusion process. For diffusion we find that mean square displacement relaxes to a constant only when the distribution of reset times possess finite mean and variance. In this case, the leading order contribution to the probability density function (PDF) of a Gaussian propagator under resetting exhibits a cusp independent of the specific details of the reset time distribution. For subdiffusion we derive the PDF in Laplace space for arbitrary resetting protocol. Resetting at constant rate allows evaluation of the PDF in terms of H function. We analyze the steady state and derive the rate function governing the relaxation behavior. For a subdiffusive process the steady state could exist even if the distribution of reset times possesses only finite mean.
我们研究了随机重置对扩散和亚扩散过程的影响。对于扩散，我们发现只有当重置时间的分布具有有限均值和方差时，均方位移才会松弛到一个常数。在这种情况下，重置下高斯传播子概率密度函数（PDF）的主导阶贡献表现出一个与重置时间分布的具体细节无关的尖点。对于亚扩散，我们推导了任意重置协议下拉普拉斯空间中的PDF。以恒定速率重置允许根据H函数评估PDF。我们分析了稳态并推导了控制松弛行为的速率函数。对于亚扩散过程，即使重置时间的分布仅具有有限均值，稳态也可能存在。
