Quantum motion with time-dependent disorder: the fluctuating-bond case

Abstract

We determine the propagation properties of a quantum particle in a d-dimensional lattice with hopping disorder, delta correlated in time. The system is delocalized: the averaged transition probability shows a diffusive behaviour. Then, superimposed on the disorder, we consider a bias favouring the motion with a given orientation, as in the dynamics of flux lines in superconductors. The result is an effective Liouvillian for the density matrix, which is characterized by competition between single-particle and pair hopping. In this case the transition probability is determined in terms of excitonic motion, each exciton being extended along the bias direction. In the small-bias regime the hopping disorder is almost ineffective along the Bragg lines of the Brillouin zone, where drift dominates. Elsewhere the system undergoes diffusion. In the opposite regime we find the single-sided-hopping spectrum, as expected from the bias term, but, due to the hopping disorder, this undergoes an abrupt change of sign at the Bragg lines.