TY - JOUR
T1 - Some fundamental aspects of Lévy flights
AU - Metzler, Ralf
AU - Chechkin, Aleksei V.
AU - Gonchar, Vsevolod Yu
AU - Klafter, Joseph
N1 - Funding Information:
RM acknowledges partial financial support through the Natural Sciences and Engineering Research Council (NSERC) of Canada and the Canada Research Chairs program of the Government of Canada. AVC acknowledges partial support from the Deutsche Forschungsgemeinschaft (DFG).
PY - 2007/10
Y1 - 2007/10
N2 - We investigate the physical basis and properties of Lévy flights (LFs), Markovian random walks with a long-tailed density of jump lengths, λ (ξ) ∼ | ξ |- 1 - α, with 0 < α < 2. In particular, we show that non-trivial boundary conditions need to be carefully posed, and that the method of images fails due to the non-locality of LFs. We discuss the behaviour of LFs in external potentials, demonstrating the existence of multimodal solutions whose maxima do not coincide with the potential minimum. The Kramers escape of LFs is investigated, and the physical nature of the a priori diverging kinetic energy of an LF is addressed.
AB - We investigate the physical basis and properties of Lévy flights (LFs), Markovian random walks with a long-tailed density of jump lengths, λ (ξ) ∼ | ξ |- 1 - α, with 0 < α < 2. In particular, we show that non-trivial boundary conditions need to be carefully posed, and that the method of images fails due to the non-locality of LFs. We discuss the behaviour of LFs in external potentials, demonstrating the existence of multimodal solutions whose maxima do not coincide with the potential minimum. The Kramers escape of LFs is investigated, and the physical nature of the a priori diverging kinetic energy of an LF is addressed.
UR - http://www.scopus.com/inward/record.url?scp=34047161047&partnerID=8YFLogxK
U2 - 10.1016/j.chaos.2007.01.055
DO - 10.1016/j.chaos.2007.01.055
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AN - SCOPUS:34047161047
SN - 0960-0779
VL - 34
SP - 129
EP - 142
JO - Chaos, Solitons and Fractals
JF - Chaos, Solitons and Fractals
IS - 1
ER -