Death of linear response and field-induced dispersion in subdiffusion

TL;DR

This paper investigates how subdiffusive continuous time random walks respond to oscillating external fields, revealing that the mean position stabilizes while dispersion grows over time due to non-stationarity.

Contribution

It demonstrates the death of linear response and introduces a field-induced dispersion effect in non-stationary subdiffusive systems with power law waiting times.

Findings

Mean particle position tends to a constant, response dies out.

Dispersion increases with time, proportional to the square of field amplitude.

Effects are observable experimentally and stem from non-stationarity.

Abstract

We discuss the response of continuous time random walks to an oscillating external field within the generalized master equation approach. We concentrate on the time dependence of the two first moments of the walker's displacements. We show that for power law waiting time distributions with 0 < alpha < 1 corresponding to a semi-Markovian situation showing nonstationarity the mean particle position tends to a constant, and the response to the external perturbation dies out. On the other hand, the oscillating field leads to a new additional contribution to the dispersion of the particle position, proportional to the square of its amplitude and growing with time. These new effects, amenable to experimental observation, result directly from the non-stationary property of the system.