Quantum backflow in biased tight-binding systems

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 system. We also evaluate the bounds on the total amount of probability that flows in the opposite direction of the particle’s momentum.

💡 Research Summary

The paper investigates quantum backflow—a non‑classical effect in which the probability current of a particle becomes negative despite the particle’s momentum being strictly positive—within one‑dimensional tight‑binding lattices that feature complex hopping amplitudes. The authors introduce a Hamiltonian of the form
(H = -\tau