Different diffusive regimes, generalized Langevin and diffusion equations

Different diffusive regimes, generalized Langevin and diffusion equations

A. A. Tateishi, E. K. Lenzi, L. R. da Silva, H. V. Ribeiro, S. Picoli Jr., R. S. Mendes, Phys. Rev. E 85, 011147 (2012). PDF | DOI

We investigate a generalized Langevin equation (GLE) in the presence of an additive noise characterized by the mixture of the usual white noise and an arbitrary one. This scenario lead us to a wide class of diffusive processes, in particular the ones whose noise correlation functions are governed by power laws, exponentials, and Mittag-Leffler functions. The results show the presence of different diffusive regimes related to the spreading of the system. In addition, we obtain a fractional diffusionlike equation from the GLE, confirming the results for long time.