TY  - JOUR
A1  - Dybiec, Bartlomiej
A1  - Capala, Karol
A1  - Chechkin, Aleksei V.
A1  - Metzler, Ralf
T1  - Conservative random walks in confining potentials
JF  - Journal of physics : A, Mathematical and theoretical
N2  - Levy 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 Levy walks move with a finite speed. Here, we present an extension of the Levy 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 Levy walk processes and will be of use in a variety of systems, for which the particles are externally confined.
KW  - Levy walk
KW  - conservative random walks
KW  - Levy flight
Y1  - 2018
U6  - https://doi.org/10.1088/1751-8121/aaefc2
SN  - 1751-8113
SN  - 1751-8121
VL  - 52
IS  - 1
PB  - IOP Publ. Ltd.
CY  - Bristol
ER  - 
TY  - JOUR
A1  - Capała, Karol
A1  - Padash, Amin
A1  - Chechkin, Aleksei V.
A1  - Shokri, Babak
A1  - Metzler, Ralf
A1  - Dybiec, Bartłomiej
T1  - Levy noise-driven escape from arctangent potential wells
JF  - Chaos : an interdisciplinary journal of nonlinear science
N2  - The escape from a potential well is an archetypal problem in the study of stochastic dynamical systems, representing real-world situations from chemical reactions to leaving an established home range in movement ecology. Concurrently, Levy noise is a well-established approach to model systems characterized by statistical outliers and diverging higher order moments, ranging from gene expression control to the movement patterns of animals and humans. Here, we study the problem of Levy noise-driven escape from an almost rectangular, arctangent potential well restricted by two absorbing boundaries, mostly under the action of the Cauchy noise. We unveil analogies of the observed transient dynamics to the general properties of stationary states of Levy processes in single-well potentials. The first-escape dynamics is shown to exhibit exponential tails. We examine the dependence of the escape on the shape parameters, steepness, and height of the arctangent potential. Finally, we explore in detail the behavior of the probability densities of the first-escape time and the last-hitting point.
Y1  - 2020
U6  - https://doi.org/10.1063/5.0021795
SN  - 1054-1500
SN  - 1089-7682
VL  - 30
IS  - 12
PB  - American Institute of Physics
CY  - Woodbury, NY
ER  -