Anomalous diffusion in nonhomogeneous media: Power spectral density of signals generated by time-subordinated nonlinear Langevin equations

摘要

Subdiffusive behavior of one-dimensional stochastic systems can be describedby time-subordinated Langevin equations. The corresponding probability densitysatisfies the time-fractional Fokker-Planck equations. In the homogeneoussystems the power spectral density of the signals generated by such Langevinequations has power-law dependency on the frequency with the exponent smallerthan 1. In this paper we consider nonhomogeneous systems and show that in suchsystems the power spectral density can have power-law behavior with theexponent equal to or larger than 1 in a wide range of intermediate frequencies.