Quantum diffusion on a dynamic disordered and harmonically driven lattice with static bias: Decoherence

Abstract

We revisit the problem of quantum diffusion of a particle moving on a lattice with dynamical disorder. Decoherence, essential for the diffusive motion, is introduced via a set of Lindblad operators, known to guarantee per se the positivity, Hermiticity and the trace-class nature of the reduced density matrix, are derived and solved analytically for several transport quantities of interest. For the special Hermitian choice of the Lindblad operators projected onto the lattice sites, we recover several known results, obtained by others, e.g. through the stochastic Liouville equation using phenomenological damping terms for the off-diagonal density-matrix elements. An interesting result that we obtained is for the case of a 1D lattice with static potential bias and a time-harmonic modulation (ac drive) of its transition-matrix element, where the diffusion coefficient shows an oscillatory behavior as function of the drive amplitude and frequency — clearly, a Wannier–Stark ladder signature. The question of dissipation is also briefly discussed.