Quantum backflow in scattering situations

TL;DR

This paper explores the quantum phenomenon of backflow, where particles can move contrary to their expected direction, revealing fundamental differences from classical physics and establishing bounds on such effects.

Contribution

It analyzes quantum backflow in scattering situations and extends the understanding of quantum inequalities related to this phenomenon.

Findings

Quantum backflow occurs in scattering scenarios.

Quantum inequalities limit the extent of backflow.

Backflow effects are observable but bounded in space and time.

Abstract

Measurable quantities that have positive values in classical dynamical systems need not to be positive in quantum theory. For example, consider a free quantum mechanical particle in one dimension. There are quantum states in which the particle's velocity is positive with probability 1, but where the probability flux for its position is locally negative; that is, while its velocity points to the right, the particle travels to the left. These effects are however small and limited in space and time by certain lower bounds, which are called "quantum inequalities". Similar effects also appear for a particle whose motion is governed by a Schroedinger equation with a certain class of potentials.