@article{
 title = {Conservative random walks in confining potentials},
 type = {article},
 year = {2019},
 keywords = {Lévy flight,Lévy walk,conservative random walks},
 volume = {52},
 id = {791d3cc5-8ff9-3ad7-a331-333bb31bb017},
 created = {2020-10-30T10:12:17.193Z},
 file_attached = {false},
 profile_id = {f5390430-7317-381a-8c56-e25a878d78ef},
 last_modified = {2020-10-30T10:12:17.193Z},
 read = {false},
 starred = {false},
 authored = {true},
 confirmed = {false},
 hidden = {false},
 private_publication = {false},
 abstract = {© 2018 IOP Publishing Ltd. Lévy walks are continuous time random walks with spatio-temporal coupling of jump lengths and waiting times, often used to model superdiffusive spreading processes such as animals searching for food, tracer motion in weakly chaotic systems, or even the dynamics in quantum systems such as cold atoms. In the simplest version Lévy walks move with a finite speed. Here, we present an extension of the Lévy walk scenario for the case when external force fields influence the motion. The resulting motion is a combination of the response to the deterministic force acting on the particle, changing its velocity according to the principle of total energy conservation, and random velocity reversals governed by the distribution of waiting times. For the fact that the motion stays conservative, that is, on a constant energy surface, our scenario is fundamentally different from thermal motion in the same external potentials. In particular, we present results for the velocity and position distributions for single well potentials of different steepness. The observed dynamics with its continuous velocity changes enriches the theory of Lévy walk processes and will be of use in a variety of systems, for which the particles are externally confined.},
 bibtype = {article},
 author = {Dybiec, B. and Capała, K. and Chechkin, A.V. and Metzler, R.},
 doi = {10.1088/1751-8121/aaefc2},
 journal = {Journal of Physics A: Mathematical and Theoretical},
 number = {1}
}

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Lévy walks are continuous time random walks with spatio-temporal coupling of jump lengths and waiting times, often used to model superdiffusive spreading processes such as animals searching for food, tracer motion in weakly chaotic systems, or even the dynamics in quantum systems such as cold atoms. In the simplest version Lévy walks move with a finite speed. Here, we present an extension of the Lévy walk scenario for the case when external force fields influence the motion. The resulting motion is a combination of the response to the deterministic force acting on the particle, changing its velocity according to the principle of total energy conservation, and random velocity reversals governed by the distribution of waiting times. For the fact that the motion stays conservative, that is, on a constant energy surface, our scenario is fundamentally different from thermal motion in the same external potentials. 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