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

TL;DR

This paper investigates how nonhomogeneous media affect the power spectral density of signals generated by time-subordinated Langevin equations, revealing potential for exponents equal to or greater than 1, unlike homogeneous systems.

Contribution

It extends the understanding of anomalous diffusion by analyzing nonhomogeneous systems and their spectral properties, showing new power-law behaviors in the PSD.

Findings

Power spectral density can have exponents ≥ 1 in nonhomogeneous media.

Spectral behavior differs significantly from homogeneous systems.

Intermediate frequency range exhibits distinct power-law behavior.

Abstract

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