Quantum backflow in biased tight-binding systems

Abstract: We study the phenomenon of quantum backflow in tight-binding systems with complex couplings, considering different boundary conditions and lattice sizes. Backflow is an intrinsically non-classical effect where the density flux associated with a particle described by the superposition of wave functions with, say, positive momentum, acquires negative values. We calculate the superposition of positive momentum states that gives rise to the strongest backflow in the systems. We also evaluate the bounds on the total amount of probability that flows in the opposite direction of the particle's momentum.