2021/10/13 by Tian Zhou, Pengbo Xu, Weihua Deng
Mathematics · Physics and Astronomy · #Amplitude #Differential Equations and Numerical Methods #Displacement (psychology) #Dynamics (music) #Electromagnetic Scattering and Analysis #Fractional Differential Equations Solutions #Function (biology) #Hermite polynomials #Kurtosis #Mathematical analysis #Mathematics #Physics #Polynomial #Position (finance) #Probability density function #Quantum mechanics #Statistical physics #Statistics #cond-mat.stat-mech #physics.class-ph #physics.data-an
paper · pdf · doi:10.1088/1751-8121/ac3f8a
published in Journal of Physics A Mathematical and Theoretical 55(2), 025001 (Institute of Physics) · 13 pages, 10 figures
arxiv created 2021/10/13 · openalex publication_date 2021/12/07 · arxiv updated 2022/01/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
Abstract Almost all the media the particles move in are non-static, one of which is the most common expanding or contracting (by a scale factor) non-static medium discussed in this paper. Depending on the expected resolution of the studied dynamics and the amplitude of the displacement caused by the non-static media, sometimes the non-static behaviors of the media can not be ignored. In this paper, we build the model describing Lévy walks in one-dimension uniformly non-static 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 non-static 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.