Continuous-time random walks in an oscillating field: Field-induced dispersion and the death of linear response

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 first two moments of the walker’s displacement and show that for power-law waiting-time distributions with 0<α<1 (corresponding to a semi-Markovian situation displaying aging) the mean particle position tends to a constant, while the response to the external perturbation dies out. The oscillating field is shown to lead to an additional new contribution to the dispersion of the particle’s position which is proportional to the square of its amplitude and grows with time.