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arXiv:2011.13644 · Physical Review A

Angular momentum quantum backflow in the noncommutative plane

Valentin Daniel Paccoia, Orlando Panella, Pinaki Roy

Published Dec 24, 2020• 16 citations
arXivHTMLPDF

Abstract

We study the quantum backflow problem in the noncommutative plane. In particular, we have considered a charged particle with and without an oscillator interaction with noncommuting momentum operators and examined angular momentum backflow in each case and how they differ from each other. We also propose a probability associated with the occurrence of angular momentum backflow and investigate whether or not the probability depends on a physical parameter, namely, the magnetic field.

DOI
10.1103/physreva.102.062218

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We study the quantum backflow problem in the noncommutative plane. In particular, we have considered a charged particle with and without an oscillator interaction with noncommuting momentum operators and examined angular momentum backflow in each case and how they differ from each other. We also propose a probability associated with the occurrence of angular momentum backflow and investigate whether or not the probability depends on a physical parameter, namely, the magnetic field.
In this paper we demonstrate a surprising aspect of quantum mechanics that is accessible to an undergraduate student. We discuss probability backflow for an electron in a constant magnetic field. It is shown that even for a wavepacket composed entirely of states with negative angular momentum the effective angular momentum can take on positive values in some regions of space. This is also a demonstration of the azimuthal angle–angular momentum uncertainty relation. This example is chosen because the backflow motion persists indefinitely. However this work can easily be extended to other systems where the motion is notionally circular, such as the hydrogen atom.
Abstract The mechanism of obtaining the fractional angular momentum by employing a trapped atom which possesses a permanent magnetic dipole moment in the background of two electric fields is reconsidered by using an alternative method. Then, we generalize this model to a noncommutative plane. We show that there are two different mechanisms, which include cooling down the atom to the negligibly small kinetic energy and modulating the density of electric charges to the critical value to get the fractional angular momentum theoretically .
Quantum backflow refers to the counterintuitive fact that the probability can flow in the direction opposite to the momentum of a quantum particle. This phenomenon has been seen to be small and fragile for one-dimensional systems, in which the maximal amount of backflow has been found to be bounded. Quantum backflow exhibits dramatically different features in two-dimensional systems that, in contrast to the one-dimensional case, allow for degenerate energy eigenstates. Here we investigate the case of a charged particle that is confined to move on a finite disk punctured at the center and that is pierced through the center, and normally to the disk, by a magnetic flux line. We demonstrate that quantum backflow can be unbounded (in a certain sense), which makes this system a promising physical platform regarding the yet-to-be-performed experimental observation of this fundamental quantum phenomenon.
We study the phenomenon of quantum backflow in tight-binding systems with complex couplings, considering different boundary conditions and lattice sizes. Backflow is an intrinsically non-classical effect where the density flux associated with a particle described by the superposition of wave functions with, say, positive momentum, acquires negative values. We calculate the superposition of positive momentum states that gives rise to the strongest backflow in the system. We also evaluate the bounds on the total amount of probability that flows in the opposite direction of the particle's momentum.
It was known that a free, non-relativistic particle in a superposition of positive momenta can, in certain cases, bear a negative probability current — hence termed quantum backflow. Here, it is shown that more variations can be brought about for a free Dirac particle, particularly when negative-energy solutions are taken into account. Since any Dirac particle can be understood as an antiparticle that acts oppositely (and vice versa), quantum backflow is found to arise in the superposition (i) of a well-defined momentum but different signs of energies, or more remarkably (ii) of different signs of both momenta and energies. Neither of these cases has a counterpart in non-relativistic quantum mechanics. A generalization by using the field-theoretic formalism is also presented and discussed.