Anomalous diffusion for a correlated process with long jumps

作者：Srokowski Tomasz^*

来源：Physica A: Statistical Mechanics and Its Applications , 2011, 390(18-19): 3077-3085.

DOI：10.1016/j.physa.2011.04.022

• Diffusion
• Jumping process
• Correlations
• Stable Levy distribution

We discuss diffusion properties of a dynamical system, which is characterised by long-tail distributions and finite correlations. The particle velocity has the stable Levy distribution; it is assumed as a jumping process (the kangaroo process) with a variable jumping rate. Both the exponential and the algebraic form of the covariance - defined for the truncated distribution - are considered. It is demonstrated by numerical calculations that the stationary solution of the master equation for the case of power-law correlations decays with time, but a simple modification of the process makes the tails stable. The main result of the paper is a finding that - in contrast to the velocity fluctuations - the position variance may be finite. It rises with time faster than linearly: the diffusion is anomalously enhanced. On the other hand, a process which follows from a superposition of the Ornstein-Uhlenbeck-Levy processes always leads to position distributions with a divergent variance which means accelerated diffusion.

• 出版日期2011-9-15