KLEIN TUNNELING IN THE PRESENCE OF RANDOM IMPURITIES
In this paper, we study Klein tunneling in random media. To this purpose, we simulate the propagation of a relativistic Gaussian wave packet through a disordered medium with randomly distributed potential barriers (impurities). The simulations, based on a relativistic quantum lattice Boltzmann (QLB) method, permit to compute the transmission coefficient across the sample, thereby providing an estimate for the conductivity (or permeability) as a function of impurity concentration and strength of the potentials. It is found that the conductivity loss due to impurities is significantly higher for wave packets of massive particles, as compared to massless ones. A general expression for the loss of conductivity as a function of the impurity percentage is presented and successfully compared with the Kozeny-Carman law for disordered media in classical fluid-dynamics.
quantum lattice boltzmann disorder media klein paradox