Quantum backflow in biased tight-binding systems

TL;DR

This paper investigates quantum backflow phenomena in biased tight-binding systems, analyzing how superpositions of positive momentum states can produce negative probability flux under various boundary conditions.

Contribution

It introduces a detailed analysis of quantum backflow in complex lattice systems, including bounds and optimal superpositions, expanding understanding of non-classical effects in discrete quantum models.

Findings

Identified superpositions causing maximum backflow.

Calculated bounds on negative probability flux.

Analyzed effects of boundary conditions and lattice size.

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