论文标题
带有二分法噪声的随机动力学：异质电报方程，异常跨界和重置
Stochastic dynamics with multiplicative dichotomic noise: heterogeneous telegrapher's equation, anomalous crossovers and resetting
论文作者
论文摘要
我们根据异质电报方程在非均匀介质中以有限的传播速度分析扩散过程。在无限速度传播的扩散极限中，我们恢复了异质扩散过程的结果。异构电报的过程表现出各种各样的扩散状态，包括高扩散，弹道运动，超扩散，正常扩散和延伸，以及观察到异常扩散系统的复杂系统的不同特征。在短时间限制中，异常扩散指数是指数的两倍，这是长时间限制的两倍，这是根据从弹道扩散到标准电报机过程中正常扩散的交叉动力学。我们还分析了存在随机泊松重置的有限速度异质扩散过程。我们表明该系统达到了非平衡固定状态。根据较大的偏差函数分析了向这种非平衡稳态的过渡。
We analyze diffusion processes with finite propagation speed in a non-homogeneous medium in terms of the heterogeneous telegrapher's equation. In the diffusion limit of infinite-velocity propagation we recover the results for the heterogeneous diffusion process. The heterogeneous telegrapher's process exhibits a rich variety of diffusion regimes including hyperdiffusion, ballistic motion, superdiffusion, normal diffusion and subdiffusion, and different crossover dynamics characteristic for complex systems in which anomalous diffusion is observed. The anomalous diffusion exponent in the short time limit is twice the exponent in the long time limit, in accordance to the crossover dynamics from ballistic diffusion to normal diffusion in the standard telegrapher's process. We also analyze the finite-velocity heterogeneous diffusion process in presence of stochastic Poissonian resetting. We show that the system reaches a non-equilibrium stationary state. The transition to this non-equilibrium steady state is analysed in terms of the large deviation function.
