Anomalous diffusion of charged particles in a lattice Lorentz gas in a transverse magnetic field

Abstract

We study diffusion in the Lorentz gas of noninteracting charged particles on a triangular lattice in a transverse magnetic field. The percolation threshold appears at the scatterers concentration ${c}_{0}=0.2155.$ The diffusion at ${c}_{0}$ is anomalous with the same exponent ${d}_{w}=2.874$ as the one found for the universality class of the standard two-dimensional lattice percolation. The presence of logarithmic corrections to the ${t}^{\ensuremath{-}2}$ algebraic tail of the velocity autocorrelation function is demonstrated in a special case for concentration of scatterers close to 1, by making use of the moment propagation technique. The results of our computer simulations show that the diffusion coefficient has a maximum above ${c}_{0},$ and the velocity autocorrelation function changes the sign of its amplitude, from negative to positive, at intermediate scatterers concentration. We employ the Boltzmann approximation and calculate the diffusion coefficient and the velocity autocorrelation function.