摘要Lévy flight with nonlinear friction is studied. Due to the occurrence of extremely long jumps Lévy flights often possess infinite variance and are physically problematic if describing the dynamics of a particle of finite mass. However, by introducing nonlinear friction, we show that the stochastic process subject to Lévy noise exhibits finite variance, leading to a well-defined kinetic energy. In the force-free field, normal diffusion behavior is observed and the diffusion coefficient decreases with Lévy index μ. Furthermore, we find a kinetic resonance of the particle in the harmonic potential to the external oscillating field in the generally underdamped region and the value of the linear friction γ0 determines whether resonance occurs or not.
Abstract：Lévy flight with nonlinear friction is studied. Due to the occurrence of extremely long jumps Lévy flights often possess infinite variance and are physically problematic if describing the dynamics of a particle of finite mass. However, by introducing nonlinear friction, we show that the stochastic process subject to Lévy noise exhibits finite variance, leading to a well-defined kinetic energy. In the force-free field, normal diffusion behavior is observed and the diffusion coefficient decreases with Lévy index μ. Furthermore, we find a kinetic resonance of the particle in the harmonic potential to the external oscillating field in the generally underdamped region and the value of the linear friction γ0 determines whether resonance occurs or not.
[1] Ott A, Bouchaud J P, Langevin D and Urbach W 1990 Phys. Rev. Lett. 65 2201
[2] Zumofen G and Klafter J 1995 Phys. Rev. E 51 2805
[3] Viswanathan G M, Afanasyev V, Buldyrev S V, Murphy E J, Prince P A and Stanley H E 1996 Nature 381 413
[4] Jespersen S, Metzler R and Fogedby H C 1999 Phys. Rev. E 59 2736
[5] Shlesinger M F, West B J and Klafter J 1987 Phys. Rev. Lett. 58 1100
[6] Chechkin A V, Klafter J, Gonchar V Y, Metzler R and Tanatarov L V 2003 Phys. Rev. E 67 010102(R)
[7] Mantegna R N and Stanley H E 1994 Phys. Rev. Lett. 73 2946
[8] Koponen I 1995 Phys. Rev. E 52 1197
[9] Chechkin A V, Gonchar V Y, Klafter J, Gonchar V Y, and Metzler R 2005 Phys. Rev. E 72 010101(R)
2011, Vol. 28 
