Classically-forbidden probability flow in the quantum reentry problem

The laws of quantum mechanics allow for a moving particle to temporarily reverse the direction of its motion even in the absence of any external force. A well-known manifestation of this counterintuitive phenomenon is the so-called quantum backflow effect, whereby the probability of finding a particle "on the left" increases with time despite the particle velocity pointing "to the right". In my talk, I will provide another clear-cut demonstration of nonconstancy of the direction of motion of a free particle. I will show that the free-space expansion of a quantum wave packet, initially confined to an interval, may be nonmonotonous: The probability density may sometimes flow back into (or reenter) the interval. The supremum of the classically-forbidden probability flow in this reentry problem appears to be the same as in the case of quantum backflow.

REFERENCE: A. Goussev, PRA 99, 043626 (2019) [https://doi.org/10.1103/PhysRevA.99.043626]