# Equivalence between quantum backflow and classically forbidden probability flow in a diffraction-in-time problem

## TL;DR

This paper demonstrates a mathematical equivalence between quantum backflow, an interference effect with negative probability flux, and classically forbidden probability flow in a diffraction-in-time scenario, linking quantum and classical phenomena.

## Contribution

It establishes a novel equivalence between quantum backflow and classical forbidden probability flow in a diffraction-in-time context.

## Key findings

- Quantum backflow is mathematically equivalent to classically forbidden probability flux.
- The effect occurs during free expansion of a matter-wave packet from a semi-infinite line.
- The work bridges quantum interference effects with classical probability flow concepts.

## Abstract

Quantum backflow is an interference effect in which a matter-wave packet comprised of only plane waves with non-negative momenta exhibits negative probability flux. Here we show that this effect is mathematically equivalent to the appearance of classically-forbidden probability flux when a matter-wave packet, initially confined to a semi-infinite line, expands in free space.