An invariant measure of chiral quantum transport

We study the invariant measure of the transport correlator for a chiral Hamiltonian and analyze its properties. The Jacobian of the invariant measure is a function of random phases. Then we distinguish the invariant measure before and after the phase integration. In the former case we found quantum diffusion of fermions and a uniform zero mode that is associated with particle conservation. After the phase integration the transport correlator reveals two types of evolution processes, namely classical diffusion and back-folded random walks. Which one dominates the other depends on the details of the underlying chiral Hamiltonian and may lead either to classical diffusion or to the suppression of diffusion.