Quantum Backflow for Many-Particle Systems

Quantum backflow is the classically-forbidden effect pertaining to the factthat a particle with a positive momentum may exhibit a negative probabilitycurrent at some space-time point. We investigate how this peculiar phenomenonextends to many-particle systems. We give a general formulation of quantumbackflow for systems formed of N free nonrelativistic structurelessparticles, either identical or distinguishable. Restricting our attention tobosonic systems where the N identical bosons are in the same one-particlestate allows us in particular to analytically show that the maximum achievableamount of quantum backflow in this case becomes arbitrarily small for largevalues of N.