Influence of the phase coherence length on ballistic transport

The characteristic length scales for the transport in disordered metals are discussed. Based on a phenomenological model of phase randomising scattering processes, the influence of the phase coherence length on the conductance of ballistic systems is studied. It is argued that the frequency dependence of the conductance of quasi-one dimensional systems can be used in order to determine not only the statistical average but the whole distribution function of the phase coherence length. Various cases of distributions, the -function, the exponential, and the Gamma distribution, are discussed. It is shown that due to quantum coherence effects deviations from the classical (Drude) behavior of the conductance exist. For independent scattering processes the probability distribution function is given by the Poisson distribution function. In this case an expression for the conductance can be derived which contains the ballistic transport, and the result for the exponential distribution.