Diffusion in a lattice of randomly placed sites and application to ac conductivity

The transition probability for a carrier hopping between randomly placed sites is determined for a system in thermodynamic equilibrium. The effect of the first waiting time is included and the result is shown to be consistent with the theory of statistical thermodynamics. Furthermore, a comparison is made with the master equation approach, which is shown to be exact when the waiting times are exponentially distributed. The application to ac conductivity is discussed.