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Physical Review A

Effects of rotation on a magnetic quadrupole moment system around a cylindrical cavity

S. L. R. Vieira, K. Bakke

Published Aug 19, 2022• 3 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.106.022211

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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.
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.
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.
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.
We explore a mesoscopic system made of a long nonconducting cylinder of inner radius [Formula: see text] where a spinless electron interacts with an attractive [Formula: see text] potential. We analyze the asymptotic behavior of the radial wave function by assuming that there is an impenetrable potential wall located at [Formula: see text], and thus, discuss the effects of rotation on the energy levels, as well as the Aharonov–Bohm effect for bound states. Further, we include a non-Hermitian operator and show that the non-Hermitian Hamiltonian has real energy eigenvalues. We also discuss the effects of rotation and the Aharonov–Bohm effect from the real energy eigenvalues. We extend our discussion to the revival time.
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.