Random walks in disordered lattice, CTRW, memory and dipole transport

TL;DR

This paper explores continuous-time random walks (CTRW) in disordered lattices, correcting derivations, analyzing memory effects, and connecting theoretical models with numerical and experimental studies of dipole transport.

Contribution

It presents corrected derivations of CTRW equations, demonstrates different memory kernel forms, and links theoretical models with numerical and experimental data on dipole transport.

Findings

Corrected CTRW derivations for dipole hopping.

Identified various memory kernel forms.

Connected theory with numerical and experimental results.

Abstract

Application of CTRW to dipole hopping transport is considered. Correct versions of derivation of the CTRW-equations are presented. Existence of different forms of memory kernels is demonstrated. Correction of Scher-Lax memory kernel within geometrical memory approach is fulfilled in accordance with leading terms of concentration expansion. Approximate solution for autocorrelation function is constructed. Modern state of numerical simulation and experimental measurements of autocorrelation function in nuclear polarization delocalization is described.