随机重置下具有轴对称幂律衰减扩散系数的非齐次平面扩散
Heterogeneous planar diffusion with axisymmetric power-law decaying diffusion coefficient under stochastic resetting
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中文总结 AI 辅助
研究随机重置下二维非齐次扩散，推导精确概率密度、稳态和首通性质，发现最优重置率并引入记忆效应。核心贡献是解析求解多种解释下的扩散问题。
中文摘要 AI 辅助
我们分析了二维各向同性非齐次扩散，其扩散系数随径向衰减，形式为$D(\rho)=D_0/\rho^2$，并受到向原点的泊松随机重置的影响。由于乘性噪声使得过程依赖于解释，我们在单一方法中处理了Itô、Stratonovich和Hänggi--Klimontovich三种解释。对于每种解释，我们获得了精确的概率密度函数、由重置诱导的非平衡稳态、均方位移以及首通性质。非平衡稳态由修正贝塞尔函数控制，并偏离了均匀扩散在重置下发现的拉普拉斯形式，而均方位移在长时间下饱和为$\langle\rho^2\rangle\sim\bar{r}^{-1/2}$，其中$\bar{r}$是重置率。到达吸收边界的中首通时间表现出一个最优重置率，在该重置率下时间最小化。此外，我们通过具有幂律核的从属（连续时间随机游走）方法纳入记忆效应，推导出分数阶Fokker--Planck方程以及非平衡稳态、通过三参数Mittag-Leffler函数表示的均方位移和首通统计；最优重置率随着记忆指数减小而增加。
英文摘要
We analyse two-dimensional isotropic heterogeneous diffusion with a radially decaying diffusion coefficient $D(ρ)=D_0/ρ^2$, subject to Poissonian stochastic resetting to the origin. Since multiplicative noise makes the process interpretation-dependent, we treat the Itô, Stratonovich, and Hänggi--Klimontovich prescriptions within a single approach. For each, we obtain the exact probability density function, the non-equilibrium stationary state induced by resetting, the mean squared displacement, and the first-passage properties. The non-equilibrium stationary state is governed by modified Bessel functions and departs from the Laplace form found for homogeneous diffusion under resetting, while the mean squared displacement saturates at long times as $\langleρ^2\rangle\sim\bar{r}^{-1/2}$, $\bar{r}$ being the resetting rate. The mean first-passage time to an absorbing boundary exhibits an optimal resetting rate at which it is minimised. In addition, we incorporate memory effects through a subordination (continuous-time random walk) approach with a power-law kernel, deriving the fractional Fokker--Planck equation together with the non-equilibrium stationary state, the mean squared displacement expressed via the three-parameter Mittag-Leffler function, and the first-passage statistics; the optimal resetting rate increases as the memory exponent decreases.
发表机构
- Research Center for Computer Science and Information Technologies, Macedonian Academy of Sciences and Arts（马其顿科学院与艺术院计算机科学与信息技术研究中心）
- Institute of Physics, Faculty of Natural Sciences and Mathematics, Ss. Cyril and Methodius University（圣西里尔和梅托迪乌斯大学自然科学与数学学院物理研究所）
- Department of Physics, Korea University（高丽大学物理系）
- Laboratoire de Physique et Chimie Théoriques (CNRS UMR 7019), Université de Lorraine Nancy（洛林大学南锡分校理论与物理化学实验室）
- Centro de Física Teórica e Computacional, Universidade de Lisboa（里斯本大学理论与计算物理中心）
- Departamento de Física, Universidade Estadual de Maringá（马里纳州立大学物理系）
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