Unbounded quantum backflow in two dimensions

TL;DR

This paper explores how quantum backflow, typically bounded in one dimension, can become unbounded in a two-dimensional system involving a charged particle on a punctured disk with magnetic flux, suggesting new experimental possibilities.

Contribution

It demonstrates that quantum backflow can be unbounded in a two-dimensional system with degeneracies, unlike the bounded case in one dimension, opening new avenues for experimental observation.

Findings

Quantum backflow is unbounded in the studied 2D system.

Degeneracy in energy eigenstates plays a key role.

The system is promising for experimental observation of backflow.

Abstract

Quantum backflow refers to the counterintuitive fact that the probability can flow in the direction opposite to the momentum of a quantum particle. This phenomenon has been seen to be small and fragile for one-dimensional systems, in which the maximal amount of backflow has been found to be bounded. Quantum backflow exhibits dramatically different features in two-dimensional systems that, contrary to the one-dimensional case, allow for degenerate energy eigenstates. Here we investigate the case of a charged particle that is confined to move on a finite disk punctured at the center and that is pierced through the center, and normally to the disk, by a magnetic flux line. We demonstrate that quantum backflow can be unbounded (in a certain sense), which makes this system a promising physical platform regarding the yet-to-be-performed experimental observation of this fundamental quantum phenomenon.