Quantum Backflow For Many-Particle Systems

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.