TY - JOUR

T1 - Lévy flights in a steep potential well

AU - Chechkin, Aleksei V.

AU - Gonchar, Vsevolod Yu

AU - Klafter, Joseph

AU - Metzler, Ralf

AU - Tanatarov, Leonid V.

PY - 2004/6

Y1 - 2004/6

N2 - Lévy flights in steeper than harmonic potentials have been shown to exhibit finite variance and a critical time at which a bifurcation from an initial monomodal to a terminal bimodal distribution occurs (Chechkin et al., Phys. Rev. E 67:010102(R) (2003)). In this paper, we present a detailed study of Lévy flights in potentials of the type U(x) α |x|c with c > 2. Apart from the bifurcation into bimodality, we find the interesting result that for c > 4 a trimodal transient exists due to the temporal overlap between the decay of the central peak around the initial δ-condition and the building up of the two emerging side-peaks, which are characteristic for the stationary state. Thus, for certain system parameters there exists a transient trimodal distribution of the Lévy flight. These properties of Lévy flights in external potentials of the power-law type can be represented by certain phase diagrams. We also present details about the proof of multimodality and the numerical procedures to establish the probability distribution of the process.

AB - Lévy flights in steeper than harmonic potentials have been shown to exhibit finite variance and a critical time at which a bifurcation from an initial monomodal to a terminal bimodal distribution occurs (Chechkin et al., Phys. Rev. E 67:010102(R) (2003)). In this paper, we present a detailed study of Lévy flights in potentials of the type U(x) α |x|c with c > 2. Apart from the bifurcation into bimodality, we find the interesting result that for c > 4 a trimodal transient exists due to the temporal overlap between the decay of the central peak around the initial δ-condition and the building up of the two emerging side-peaks, which are characteristic for the stationary state. Thus, for certain system parameters there exists a transient trimodal distribution of the Lévy flight. These properties of Lévy flights in external potentials of the power-law type can be represented by certain phase diagrams. We also present details about the proof of multimodality and the numerical procedures to establish the probability distribution of the process.

KW - Classical transport

KW - Random walks and Lévy flights

KW - Stochastic analysis methods (Fokker-Planck, Langevin, etc.)

KW - Stochastic processes

UR - http://www.scopus.com/inward/record.url?scp=3543074105&partnerID=8YFLogxK

U2 - 10.1023/b:joss.0000028067.63365.04

DO - 10.1023/b:joss.0000028067.63365.04

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AN - SCOPUS:3543074105

SN - 0022-4715

VL - 115

SP - 1505

EP - 1535

JO - Journal of Statistical Physics

JF - Journal of Statistical Physics

IS - 5-6

ER -