Brownian motion in one-dimensional disordered systems

Abstract

The Brownian motion of a particle in a one-dimensional random potential of Wiener-Levy type is studied Thermal fluctuations exert random forces or transfer random energies which set the particle in Brownian motion. These two kinds of noise provide different asymptotic space (L)-time (t) scaling relations : L ~ ln2 t or L ~ tν. The application of this model to a single domain wall is discussed and the expression of low frequency magnetic susceptibility and electrical conductivity are established and possible comparisons with experiments are discusse