Quantum backflow and scattering

Abstract

Backflow is the phenomenon that the probability current of a quantum particle on the line can flow in the direction opposite to its momentum. In this article, previous investigations of backflow, pertaining to interaction-free dynamics or purely kinematical aspects, are extended to scattering situations in short-range potentials. It is shown that backflow is a universal quantum effect which exists in any such potential, and is always of bounded spatial extent in a specific sense. The effects of reflection and transmission processes on backflow are investigated, both analytically for general potentials, and numerically in various concrete examples.Comment: minor changes, as published in Phys. Rev. A; 13 pages, 11 figures, 3 videos, computer cod

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

“…(11), propagates in free space, Eq. (12). We have shown that the formula giving the backflow probability against a force mg ≥ 0 during a time interval (T 1 , T 2 ), Eq.…”

Decay of a quasistable quantum system and quantum backflow

“…Since backflow is purported to be a universal quantum effect, existing in an interaction-free environment as well as in the presence of short-range potentials [16], we further elucidate the decaying behaviour of the preceding section by examining the time evolution of a free wave packet initially confined to the region r ∈ (0, a). To do so we first need the S-wave partial-wave propagator of a free particle.…”

“…Recently it was shown that quantum backflow is a universal quantum effect; it does not only pertain to interaction-free systems, but can be extended to scattering involving short-range potentials [16]. Moreover, Goussev [17] demonstrates the equivalence between quantum backflow of a wave packet consisting of nonnegative momentum components and the reentry problem in which a free wave packet initially confined to a semi-infinite line, but unconstrained in momentum space, evolves in time to lower and, for certain intervals, to raise the probability of being in the confined space region.…”

Probability backflow for correlated quantum states

“…Some aspects of the spatial extent of QB were studied in Refs. [7,12,13]. Probability backflow in quantum systems with rotational motion, such as an electron in a constant magnetic field, was addressed in Ref.…”

“…[15]. QB has been also investigated under the action of a constant force [16], in the presence of spin-orbit coupling [17], thermal noise [18], and dissipations [19] and in scattering situations [13]. QB in relativistic quantum mechanics was studied in Refs.…”