非线性阻尼驱动的莱维飞行动力学性质  

Dynamical mechanism of Lévy flight driven by the nonlinear friction

作　　者：刘剑[1,2] 陈晓白[1] 徐登辉[1] 李熊[1] 陈晓松[2] 杨波[2] 

机构地区：[1]北京工商大学理学院,北京100048 [2]中国科学院理论物理研究所理论物理前沿重点实验室,北京100190

出　　处：《物理学报》2016年第16期50-56,共7页Acta Physica Sinica

基　　金：国家自然科学基金(批准号:11547231;61405003;11404013)资助的课题~~

摘　　要：基于动力学连续时间无规行走方法,对受非线性阻尼驱动的莱维飞行在自由势场以及周期势场中的扩散行为进行了研究.非线性阻尼取代斯托克斯阻尼,通过动力学连续时间无规行走方法体现在莱维随机行走粒子的每一步跳跃中.结果显示,非线性阻尼的强阻尼耗散作用导致莱维飞行的超扩散行为衰减为正常扩散,粒子速度定态分布呈现双峰与单峰的相互转化.周期势场的束缚作用会导致粒子扩散达到一个稳定态,而莱维粒子自身性质会使粒子存在极小概率跃出周期势阱的跳跃行为,表现为方均位移随时间的演化出现跃迁现象.As a basic problem, anomalous diffusions in various fields of physics and related science have been studied for several decades. One of the topic problems of anomalous diffusion is Levy flight, which is employed as the statistical model to solve the problems in various fields. Therefore, studying the dynamical mechanism of Levy flight, especially in the existence of external potential, is of importance for relative theoretical and experimental research. In this paper, within the framework of dynamical continuous time random walk method, the Levy flight diffusive behaviors and dynamical mechanisms driven by nonlinear friction are studied in the force-free potential and periodic potential. The nonlinear friction instead of Stokes friction is considered in each step of Levy random walker through the dynamical continuous time random walk method. In the force-free potential, the nonlinear friction term can be considered to be inharmonic potential in the velocity space which can restrain the velocity of random walker, so the anomalous superdiffusion of Levy flight turns into a behavior in the normal case because of the strong dissipative effect of the nonlinear friction. Due to the introduction of the nonlinear friction, the velocity steady probability density distribution behaves as transitions between bimodal shape and unimodal shape, which is detrmined by the Levy index μ and the friction indexes γ0 andγ2. The bimodality is most pronounced at μ = 1, with μ increasing the bimodality becomes weaker, and vanishes at μ=2 which is the Gaussian case. Besides, there is a critical value γ0c =0.793701, which also determines the bimodal behaviors. Forγ0=0 the bimodality is most pronounced, asγ0 increases it smooths out and turns into a unimodal one forγ0〉γ0c. In the existence of periodic potential, the Levy random walker can be captured by the periodical potential due to the introduction of nonlinear friction, which behaves as the mean square displacement ？δx2（t）？ of the random walker and can reach a ste

关 键 词：动力学连续时间无规行走 非线性阻尼 莱维飞行 周期势场 

分 类 号：O552.2[理学—热学与物质分子运动论]