On the frequency dependence of the conductivity in random walk models with internal states

Abstract

The random walk of a particle in two models of an ideal lattice with internal states has been studied. In the first model one vertical ladder of energy levels exists at each lattice site, in the second model different ladders of levels lead to neighboring sites. In thermal equilibrium, the mobility of the particle was found frequency-independent in the first model and frequency-dependent in the second. The continuous-time random walk (CTRW) description of both models has been investigated. The waiting-time distribution for the first case has been obtained analytically in the Laplace domain. An example for φ (t) has been calculated numerically by inverse Laplace transformation. In the second case an extension of the CTRW description to a backward jump model has been performed and the corresponding waiting-time distributions have been calculated.