Fractal time random walk and subrecoil laser cooling considered as renewal processes with infinite mean waiting times
arXiv:cond-mat/0407481 · doi:10.1007/1-4020-2947-0_12
Abstract
There exist important stochastic physical processes involving infinite mean waiting times. The mean divergence has dramatic consequences on the process dynamics. Fractal time random walks, a diffusion process, and subrecoil laser cooling, a concentration process, are two such processes that look qualitatively dissimilar. Yet, a unifying treatment of these two processes, which is the topic of this pedagogic paper, can be developed by combining renewal theory with the generalized central limit theorem. This approach enables to derive without technical difficulties the key physical properties and it emphasizes the role of the behaviour of sums with infinite means.
arXiv comment9 pages, 7 figures, to appear in the Proceedings of Cargese Summer School on "Chaotic dynamics and transport in classical and quantum systems"