Lévy walk dynamics in nonstatic media
Abstract
Almost all the media the particles move in are nonstatic, one of which is the most common expanding or contracting (by a scale factor) nonstatic medium discussed in this paper. Depending on the expected resolution of the studied dynamics and the amplitude of the displacement caused by the nonstatic media, sometimes the nonstatic behaviors of the media can not be ignored. In this paper, we build the model describing Lévy walks in onedimension uniformly nonstatic media, where the physical and comoving coordinates are connected by scale factor. We derive the equation governing the probability density function of the position of the particles in comoving coordinate. Using the Hermite orthogonal polynomial expansions, some statistical properties are obtained, such as mean squared displacements (MSDs) in both coordinates and kurtosis. For some representative nonstatic media and Lévy walks, the asymptotic behaviors of MSDs in both coordinates are analyzed in detail. The stationary distributions and mean first passage time for some cases are also discussed through numerical simulations.
 Publication:

Journal of Physics A Mathematical General
 Pub Date:
 January 2022
 DOI:
 10.1088/17518121/ac3f8a
 arXiv:
 arXiv:2110.07715
 Bibcode:
 2022JPhA...55b5001Z
 Keywords:

 mean first passage time;
 nonstatic media;
 stationary distributions;
 Condensed Matter  Statistical Mechanics;
 Physics  Classical Physics;
 Physics  Data Analysis;
 Statistics and Probability
 EPrint:
 13 pages, 10 figures