Gaussian diffusion interrupted by Lévy walk. (5th October 2016)

• Record Type: Journal Article
• Authors: Weber, Piotr; Pepłowski, Piotr
• Is Part Of: Journal of statistical mechanics. (2016:Oct.)
• Publication Date: 2016-10-05
• Subjects: Statistical mechanics -- Periodicals; Mechanics -- Statistical methods -- Periodicals; 530.1305
• DOI: 10.1088/1742-5468/2016/10/103202
• Languages: English
• ISSNs: 1742-5468

Abstract

Abstract: We investigate a stochastic process that links two processes in one model: Gaussian diffusion and one-sided Levy walks leading to anomalous diffusion. The motivation for our study is an observation of 'heavy-tailed' momentum probability density in a standard map and its modifications when accelerated modes emerge in the phase space. In this stochastic model, we derive a fractional differential equation for its probability density function. Numerical and analytical solutions for certain values of parameters are presented.