Specific features of the effect of time dependent field on subdiffusing particles. The stochastic Liouville equation approach

TL;DR

This paper investigates how time-dependent external fields influence subdiffusive particles using a stochastic Liouville equation approach, providing exact formulas for moments and revealing unusual phase-dependent behaviors.

Contribution

It introduces a rigorous Markovian representation method for analyzing non-Markovian CTRW under time-dependent fields, specifically applied to subdiffusive migration.

Findings

Exact formulas for first and second moments derived

Unusual phase dependence observed in oscillating fields

Revealed anomalous field-dependent contributions

Abstract

We analyze the effect of 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. The method is applied to the case of subdiffusive migration in which the exact formulas for the first and second moments of spatial distribution are derived. For oscillating external field they predict unusual dependence of the first moment on oscillation phase and anomalous field dependent contribution to