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Proceedings of the Royal Society A Mathematical Physical and Engineering Sciences

Persistent currents, revival time and effects of rotation on an attractive inverse-square-type potential in a magnetic quadrupole moment system

S. L. R. Vieira, K. Bakke

Published May 1, 2023• 4 citations
Publisher

Abstract

We study the appearance of an Aharonov–Bohm-type effect around a cylindrical cavity in a magnetic quadrupole moment system in a rotating reference frame. The analogue of the Aharonov–Bohm-type effect of bound states arises from the interaction of the magnetic quadrupole moment of a neutral particle with an induced electric field when the neutral particle is subject to an attractive inverse-square-type potential, which in turn stems from the interaction of the magnetic quadrupole moment of a neutral particle with a magnetic field. We also discuss how the effects of rotation modify the degeneracy of the energy levels in contrast to the case of absence of rotation. Besides this, we calculate the revival time and the persistent currents.

DOI
10.1098/rspa.2022.0848

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We study the appearance of an Aharonov–Bohm-type effect around a cylindrical cavity in a magnetic quadrupole moment system in a rotating reference frame. The analogue of the Aharonov–Bohm-type effect of bound states arises from the interaction of the magnetic quadrupole moment of a neutral particle with an induced electric field when the neutral particle is subject to an attractive inverse-square-type potential, which in turn stems from the interaction of the magnetic quadrupole moment of a neutral particle with a magnetic field. We also discuss how the effects of rotation modify the degeneracy of the energy levels in contrast to the case of absence of rotation. Besides this, we calculate the revival time and the persistent currents.
We analyze the interaction of the magnetic quadrupole moment of a neutral particle with magnetic and electric fields around a cylindrical cavity in a rotating reference frame. In contrast to the energy levels yielded by a Coulomb-type potential that stems from the interaction of the magnetic quadrupole moment with a nonuniform magnetic field, we show that the effects of rotation break the degeneracy of the energy levels. Moreover, we show that the effects of rotation can gives rise to an Aharonov-Bohm-type effect. Further, we discuss the appearance of persistent currents and the revival time.
The behavior of a neutral particle with magnetic quadrupole moment that interacts with axial magnetic and electric fields is analyzed. From the interaction of the magnetic quadrupole moment with the axial magnetic field, a spectrum of energy analogous to a Coulomb potential in two dimensions is obtained. Furthermore, the presence of an axial electric field is also considered. From the interaction of the magnetic quadrupole moment with this electric field, an analog of the Aharonov-Bohm effect is obtained. Finally, the Aharonov-Bohm effect for bound states is analyzed when this neutral particle system is subject to the two-dimensional harmonic oscillator.
From the interaction between the magnetic quadrupole moment of a neutral particle (atom or molecule) with a radial electric field, a uniform effective magnetic field perpendicular to the plane of motion of the neutral particle appears. In addition, it is considered that the presence of a scalar potential is proportional to the radial distance and noninertial effects that stem from a rotating reference frame. Then, analytical solutions to the Schrödinger equation are obtained, where it is shown that the Landau-type levels are modified, and the allowed values of the cyclotron frequency are determined by the angular velocity of the rotating frame, the parameter associated with the scalar potential proportional to the radial distance and the quantum numbers of the system.
We study the analogue of the Aharonov–Bohm effect for bound states for a neutral particle with a permanent magnetic dipole moment interacting with an external field. We consider a neutral particle confined to moving between two coaxial cylinders and show the dependence of the energy levels on the Aharonov-Casher quantum flux. Moreover, we show that the same flux dependence of the bound states can be found when the neutral particle is confined to a one-dimensional quantum ring and a quantum dot, and we also calculate the persistent currents in each case.
Abstract We investigate quantum effects on a nonrelativistic neutral particle with a permanent magnetic dipole moment that interacts with an electric field. This neutral particle is also under the influence of a background that breaks the Lorentz symmetry. We focus on the Lorentz symmetry violation background determined by a space-like vector field. Then, we show that the effects of the violation of Lorentz symmetry can yield an attractive Coulomb-type potential. Furthermore, we obtain the bound state solutions to the Schrödinger–Pauli equation and show that the spectrum of energy is a function of the Aharonov–Casher geometric quantum phase. Finally, we discuss the arising of persistent spin currents.
The quantum dynamics of a moving particle with a magnetic quadrupole moment that interacts with electric and magnetic fields is introduced. By dealing with the interaction between an electric field and the magnetic quadrupole moment, it is shown that an analogue of the Coulomb potential can be generated and bound state solutions can be obtained. Besides, the influence of the Coulomb-type potential on the harmonic oscillator is investigated, where bound state solutions to both repulsive and attractive Coulomb-type potentials are achieved and the arising of a quantum effect characterized by the dependence of the harmonic oscillator frequency on the quantum numbers of the system is discussed.