非齐次环境中的Lévy游动
Lévy walks in nonhomogeneous environments
摘要：
讨论了带余项的Lévy行走过程。跳跃时间是由$α$ -稳定的分布与$α>1$，而等待时间分布是泊松分布，并涉及一个位置依赖率，反映了非均匀的陷阱分布。主方程的推导和解决的渐近极限的幂律形式的跳跃率。静止粒子和飞行粒子的相对密度随时间变化，在大的时间范围内，两种分布的渐近形式都服从拉伸指数分布。扩散性质进行了讨论，它表明，由于异质陷阱结构，增强扩散，观察到的均匀的情况下，可能会变成一个subdiffusion。密度分布和均方位移也评价从蒙特卡罗模拟的个人轨迹。
英文摘要：
The Lévy walk process with rests is discussed. The jumping time is governed by an $α$-stable distribution with $α>1$ while a waiting time distribution is Poissonian and involves a position-dependent rate which reflects a nonhomogeneous trap distribution. The master equation is derived and solved in the asymptotic limit for a power-law form of the jumping rate. The relative density of resting and flying particles appears time-dependent and the asymptotic form of both distribution obey a stretched-exponential shape at large time. The diffusion properties are discussed and it is demonstrated that, due to the heterogeneous trap structure, the enhanced diffusion, observed for the homogeneous case, may turn to a subdiffusion. The density distributions and mean squared displacements are also evaluated from Monte Carlo simulations of individual trajectories.
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