Theoretical And Numerical Study Of Lévy Walk

The Levy walk that the time and space are coupled is one of special model of CTRW, and is the process with continuous sample paths which arises from consecu-tive linear motions of independent identically distributed lengths and directions. This paper is based on the classical symmetrical one-dimensional Levy walk. Assume that the particle’s waiting time is power law, i.e. ψ(t)～t-λ-1,0< λ< 3. And the size of the velocity is constant, but the direction is random. On theoretical aspect, we will discuss the particles’fractional order moments from the view of probability density function of the symmetrical one-dimensional Levy walk. Then discuss the diffusion behavior of the unsymmetrical one-dimensional Levy walk. After this, we will discuss the isotropous of the particles under the two-dimension case. In the aspect of numer-ical simulation, we verify these result. And finally, will give the application in the uncertainties Hamiltonian system.