Effect of a time-dependent field on subdiffusing particles

We analyze the effect of a time-dependent external field on non-Markovian migration described by the continuous time random walk (CTRW) approach. The rigorous method of treating the problem is proposed which is based on the Markovian representations of the CTRW approach and field modulation. With the use of this method we derive the non-Markovian stochastic Liouville equation (SLE), that describes the effect of this field, and thoroughly analyze the relation of the derived SLE with equations proposed earlier. This SLE is applied to the case of subdiffusive migration in which the exact formulas for the first and second moments of spatial distribution are obtained. In the case of oscillating external field they predict unusual dependence of the first moment on oscillation phase and anomalous time behavior of field dependent contribution to the dispersion which agree with results of earlier works. Anomalous time dependence is also found in the case of a fluctuating field. The specific features of this time dependence are analyzed in detail.