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arXiv:0902.1474 · Physical Review A

Relativistic Landau quantization for a neutral particle

K. Bakke, Claudio Furtado

Published Sep 10, 2009• 57 citations
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Abstract

In this contribution we study the Landau levels arising within the relativistic quantum dynamics of a neutral particle with a permanent magnetic dipole moment interacting with an external electric field. We consider the Aharonov-Casher coupling of the magnetic dipole to the electric field and investigate an analog of Landau quantization in this system for two different field configurations. In both cases we obtain the eigenfunctions and eigenvalues of the Hamiltonian.

DOI
10.1103/physreva.80.032106

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In this contribution we study the Landau levels arising within the relativistic quantum dynamics of a neutral particle with a permanent magnetic dipole moment interacting with an external electric field. We consider the Aharonov-Casher coupling of the magnetic dipole to the electric field and investigate an analog of Landau quantization in this system for two different field configurations. In both cases we obtain the eigenfunctions and eigenvalues of the Hamiltonian.
In this work, we investigate the system in which a neutral particle with magnetic dipole momentum interacts with an external electric field subject to the central potentials, such as scalar potentials proportional to the radial distance and Coulomb like potential. In addition, we analyse the same system when it is confined to a two-dimensional quantum ring and to a quantum dot. In the search for analytical solutions for the Schrödinger-Pauli equation we show that the energy states for this system of a neutral particle subject to the central potentials depend on the quantum geometric phase φAC and the quantum numbers associated with the radial modes, angular momentum, and spin of the system {n, l, s}. Furthermore, we present the quantization of Landau for a neutral particle with a permanent magnetic dipole moment in the presence of external fields and under the influence of a Coulomb like potential. We use the idea of Ericsson e Sjöqvist which consists in using the system proposed by Aharonov and Casher to generate an analogue of the quantization of Landau for neutral atom systems. Moreover, we observe that when the analogue of the Landau quantization is subject to a Coulomb like potential its cyclotron frequency is modified in contrast with the behavior found by of reference. Finally, we discuss the quantum effect characterized by the dependence of quantum numbers with the angular frequency.
We study the quantum dynamics of a neutral particle that posseses a permanent magnetic and electric dipole moments in the presence of an electromagnetic field. The analysis of this dynamics demonstrates the appearance of a quantum phase that combines the Aharonov-Casher effect and the He-Mckellar-Wilkens effect. We demonstrate that this phase is a special case of the geometric quantum phase. A series of field configurations where this phase would be found is presented. A generalized Casella-type effect is found in one of these configurations. A physical scenario for the quantum phase in an interferometric experiment is proposed.
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.
In this paper we study the quantum dynamics of a neutral particle in the presence of a topological defect. We investigate the appearance of a geometric phase in the relativistic quantum dynamics of a neutral particle which possesses permanent magnetic and electric dipole moments in the presence of an electromagnetic field in this curved space-time. The nonrelativistic quantum dynamics are investigated using the Foldy-Wouthuysen expansion. The gravitational Aharonov-Casher and He-McKellar-Wilkens effects are investigated for a series of electric and magnetic field configurations.