Liu, J (reprint author), Beijing Technol & Business Univ, Sch Sci, Beijing 100048, Peoples R China.
; Liu, J (reprint author), Chinese Acad Sci, Inst Theoret Phys, State Key Lab Theoret Phys, Beijing 100190, Peoples R China.

文章类型:

Article

英文摘要:

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 mu and the friction indexes gamma(0) and gamma(2). The bimodality is most pronounced at mu= 1, with mu increasing the bimodality becomes weaker, and vanishes at mu= 2 which is the Gaussian case. Besides, there is a critical value gamma(0c) = 0.793701, which also determines the bimodal behaviors. For gamma(0) = 0 the bimodality is most pronounced, as gamma(0) increases it smooths out and turns into a unimodal one for gamma(0) > gamma(0c). 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. . of the random walker and can reach a steady state quite quickly after a short lag time. However, the restraint is not equivalent to truncation procedures. Since the velocity of random walker obeys Levy distribution, there is still extremely large jump length for random walker with extremely small probability. When the extremely large jump length is long enough and the barrier height U-0 is not comparably high, the random walker can cross the barrier height of the periodic potential and jump out of the periodic potential, which behaves as the mean square displacement . and a leap from a steady state to another one appears. However, the restraint on the random walker from the nonlinear friction always exists, so the random walker is captured again by the periodic potential, which means that the mean square displacement comes into a steady state again.