Quantum backflow for many-particle systems

TL;DR

This paper explores quantum backflow in many-particle systems, providing a general formulation and showing that the maximum backflow diminishes as the number of bosons increases, highlighting a collective suppression effect.

Contribution

It extends the concept of quantum backflow to many-particle systems and analytically demonstrates the diminishing backflow with increasing particle number in bosonic states.

Findings

Quantum backflow is formulated for N-particle systems.

Maximum backflow decreases with larger N in bosonic states.

Analytical results show suppression of backflow in large bosonic systems.

Abstract

Quantum backflow is the classically-forbidden effect pertaining to the fact that a particle with a positive momentum may exhibit a negative probability current at some space-time point. We investigate how this peculiar phenomenon extends to many-particle systems. We give a general formulation of quantum backflow for systems formed of $N$ free nonrelativistic structureless particles, either identical or distinguishable. Restricting our attention to bosonic systems where the $N$ identical bosons are in the same one-particle state allows us in particular to analytically show that the maximum achievable amount of quantum backflow in this case becomes arbitrarily small for large values of $N$.