Numerical evidence of Sinai diffusion of random-mass Dirac particles

TL;DR

This study uses quantum lattice Boltzmann simulations to demonstrate Sinai diffusion in Dirac particles with random mass, revealing localization and ultra-slow diffusion due to quantum interference effects.

Contribution

First numerical evidence of Sinai diffusion in quantum-relativistic particles with random mass using quantum lattice Boltzmann methods.

Findings

Evidence of localization and ultra-slow Sinai diffusion.

Quantum interference causes opposite wave branches to localize.

Quantum lattice Boltzmann scheme is effective for simulating quantum transport.

Abstract

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.