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arXiv:1603.01518 · The Journal of Chemical Physics

Rotating effects on the Landau quantization for an atom with a magnetic quadrupole moment

I. C. Fonseca, K. Bakke

Published Jan 6, 2016• 22 citations
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Abstract

Based on the single particle approximation [Dmitriev et al., Phys. Rev. C 50, 2358 (1994) and C.-C. Chen, Phys. Rev. A 51, 2611 (1995)], the Landau quantization associated with an atom with a magnetic quadrupole moment is introduced, and then, rotating effects on this analogue of the Landau quantization is investigated. It is shown that rotating effects can modify the cyclotron frequency and breaks the degeneracy of the analogue of the Landau levels.

DOI
10.1063/1.4939525

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Based on the single particle approximation [Dmitriev et al., Phys. Rev. C 50, 2358 (1994) and C.-C. Chen, Phys. Rev. A 51, 2611 (1995)], the Landau quantization associated with an atom with a magnetic quadrupole moment is introduced, and then, rotating effects on this analogue of the Landau quantization is investigated. It is shown that rotating effects can modify the cyclotron frequency and breaks the degeneracy of the analogue of the Landau levels.
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 quantum dynamics of an atom with a magnetic quadrupole moment that interacts with an external field subject to harmonic and linear confining potentials is investigated. It is shown that the interaction between the magnetic quadrupole moment and an electric field gives rise to an analogue of the Coulomb potential and, by confining this atom to harmonic and linear confining potentials, a quantum effect characterized by the dependence of the angular frequency on the quantum numbers of the system is obtained. In particular, it is shown that the possible values of the angular frequency associated with the ground state of the system are determined by a third-degree algebraic equation.
The behaviour of a neutral particle (atom, molecule) with an induced electric dipole moment in a region with a uniform effective magnetic field under the influence of the Kratzer potential (Kratzer 1920 Z. Phys. 3 , 289–307. ( doi:10.1007/BF01327754 )), and rotating effects is analysed. It is shown that the degeneracy of the Landau-type levels is broken and the angular frequency of the system acquires a new contribution that stems from the rotation effects. Moreover, in the search for bound state solutions, it is shown that the possible values of this angular frequency of the system are determined by the quantum numbers associated with the radial modes and the angular momentum, the angular velocity of the rotating frame and by the parameters associated with the Kratzer potential.
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 will show that when a neutral particle with permanent electric dipole moment interacts with a specific field configuration when the local reference frames of the observers are Fermi-Walker transported, the Landau quantization analog to the He-McKellar-Wilkens setup arises in the nonrelativistic quantum dynamics of the neutral particle due the noninertial effects of the Fermi-Walker reference frame. We show that the noninertial effects do not break the infinity degeneracy of the energy levels, but in this case, the cyclotron frequency depends on the angular velocity.
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.