Chechkin Aleksei V, Hofmann Michael, Sokolov Igor M
School of Chemistry, Tel Aviv University, Ramat Aviv, 69978 Tel Aviv, Israel.
Phys Rev E Stat Nonlin Soft Matter Phys. 2009 Sep;80(3 Pt 1):031112. doi: 10.1103/PhysRevE.80.031112. Epub 2009 Sep 10.
Based on the Langevin description of the continuous time random walk (CTRW), we consider a generalization of CTRW in which the waiting times between the subsequent jumps are correlated. We discuss the cases of exponential and slowly decaying persistent power-law correlations between the waiting times as two generic examples and obtain the corresponding mean squared displacements as functions of time. In the case of exponential-type correlations the (sub)diffusion at short times is slower than in the absence of correlations. At long times the behavior of the mean squared displacement is the same as in uncorrelated CTRW. For power-law correlations we find subdiffusion characterized by the same exponent at all times, which appears to be smaller than the one in uncorrelated CTRW. Interestingly, in the limiting case of an extremely long power-law correlations, the (sub)diffusion exponent does not tend to zero, but is bounded from below by the subdiffusion exponent corresponding to a short-time behavior in the case of exponential correlations.
基于连续时间随机游走（CTRW）的朗之万描述，我们考虑对CTRW进行一种推广，其中后续跳跃之间的等待时间是相关的。我们讨论了等待时间之间指数型和缓慢衰减的持久幂律相关性这两种一般情况，并得到了相应的均方位移作为时间的函数。在指数型相关性的情况下，短时间内的（次）扩散比无相关性时更慢。长时间时，均方位移的行为与无相关性的CTRW相同。对于幂律相关性，我们发现次扩散在所有时间都具有相同的指数特征，该指数似乎比无相关性的CTRW中的指数小。有趣的是，在极长幂律相关性的极限情况下，（次）扩散指数并不趋于零，而是由指数相关性情况下对应短时间行为的次扩散指数从下方界定。
