Quantum Walks in Weak Stochastic Gauge Fields

The behaviour of random quantum walks is known to be diffusive. Here we study discrete time quantum walks in weak stochastic gauge fields. In the case of position and spin dependent gauge field, we observe a transition from ballistic to diffusive motion, with the probability distribution becoming Gaussian. However, in contradiction to common belief, weak stochastic electric gauge fields reveal the persistence of Bloch oscillations despite decoherence which we demonstrate on simulations and prove analytically. The proposed models provide insights into the interplay between randomness and coherent dynamics of quantum walks.