  We present quantum Lattice Boltzmann simulations of the Dirac equation for
quantum-relativistic particles with random mass. By choosing zero-average
random mass fluctuation, the simulations show evidence of localization and
ultra-slow Sinai diffusion, due to the interference of oppositely propagating
branches of the quantum wavefunction which result from random sign changes of
the mass around a zero-mean. The present results indicate that the quantum
lattice Boltzmann scheme may offer a viable tool for the numerical simulation
of quantum-relativistic transport phenomena in topological materials.
