Transition to a microscopic diffusion regime and dimensional crossover in a disordered conductor

The low-temperature behaviour of the resistance of indium oxide samples is discussed within the framework of localisation theories. It is demonstrated that, in three dimensions, the interplay between the effective inelastic diffusion length l_in and the correlation length xi determines the nature of the diffusion process. A crossover to two-dimensional behaviour is observed once l_in becomes comparable with the sample thickness.