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Analog of landau Levels to Electric Dipole

Leandro Rodrigo Ribeiro, Claudio Furtado, Jose Roberto Nascimento

Published Feb 21, 2005• 0 citations
OpenAlex

Abstract

In this article we discuss the analogy between the dynamics of a neutral particle with an electric dipole, in the presence of configuration of magnetic field, with Landau level quantization for charged particle. We analyze this quantization based on the He-Mckelar-Wilkens interaction developed of similar way that Ericsson and Sj\\"oqvist[Phys Rev. A {\\bf 65} 013607 (2001)] was analyzed the Landau-Aharonov-Casher effect. The energy level and eingenfuctions and eigenvalues are obtained.

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In this article we discuss the analogy between the dynamics of a neutral particle with an electric dipole, in the presence of configuration of magnetic field, with Landau level quantization for charged particle. We analyze this quantization based on the He-Mckelar-Wilkens interaction developed of similar way that Ericsson and Sj\"oqvist[Phys Rev. A {\bf 65} 013607 (2001)] was analyzed the Landau-Aharonov-Casher effect. The energy level and eingenfuctions and eigenvalues are obtained.
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 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 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 analyse the physical meaning of quantum phase effects for point-like charges and electric (magnetic) dipoles in an electromagnetic (EM) field. At present, there are known eight effects of such a kind: four of them (the magnetic and electric Aharonov – Bohm phases for electrons, the Aharonov – Casher phase for a moving magnetic dipole and the He – McKellar – Wilkens phase for a moving electric dipole) had been disclosed in 20th century, while four new quantum phases had recently been found by our team (A. L. Kholmetskii, O. V. Missevitch, T. Yarman). In our analysis of physical meaning of these phases, we adopt that a quantum phase for a dipole represents a superposition of quantum phases for each charge, composing the dipole. In this way, we demonstrate the failure of the Schrödinger equation for a charged particle in an EM field to describe new quantum phase effects, when the standard definition of the momentum operator is used. We further show that a consistent description of quantum phase effects for moving particles is achieved under appropriate re-definition of this operator, where the canonical momentum of particle in EM field is replaced by the interactional EM field momentum. Some implications of this result are discussed.