TY - JOUR T1 - Numerical Evidence of Sinai Diffusion of Random-Mass Dirac Particles JO - Communications in Computational Physics VL - 4 SP - 899 EP - 909 PY - 2018 DA - 2018/04 SN - 23 DO - http://doi.org/10.4208/cicp.OA-2016-0239 UR - https://global-sci.org/intro/article_detail/cicp/11198.html KW - Sinai diffusion, Anderson localization, QLB method, Dirac equation, random mass. AB -

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.