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Efeitos não-inerciais em Anéis Quânticos

Lincoanderson Oliveira Dantas

Published Mar 26, 2015• 0 citations

Abstract

In this thesis, we investigate by the first time the impact of non-inertial effects associated with the rotation of the reference system on charged and neutral particles confined by a quantum ring, which is described by the potential of Tan-Inkson. The contribution of the rotation is introduced by its coupling with angular momentum of the system. We show that the rotation is introduced via a non-minimum coupling to the kinetic part of the Hamiltonian describing the quantum dynamics of systems studied here. Thus, we show that non-inertial effects of the rotation induce on the quantum properties of the particles similar effects generated by a magnetic field. We also investigated the contribution of a screw dislocation on the physical properties of the particles. The topological defect contributes as a torsion source, presenting a contribution similar to the Aharonov-Bohm flux. Besides charged particles (electrons and holes), we also study the effects of rotation on neutral particles in three different scenarios: a neutral particle with a permanent magnetic dipole moment coupled by the Aharanov-Casher interaction; a neutral particle with a permanent electric dipole moment coupled by the interaction proposed by He-McKellar-Wilkens and a neutral particle with an electric dipole moment induced by the field configuration proposed by Wei-Han-Wei. In all three cases it is shown the similarity between the neutral and charged particles. We analyze the non-relativistic quantum dynamics of these particles by solving the Schrödinger equation. In addition to the energy spectrum and wave functions, we calculate the persistent current and the magnetization for the four systems studied here, and we also analyzed, from the expression for the persistent current for quantum rings, the limit case for quantum dots.

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In this thesis, we investigate by the first time the impact of non-inertial effects associated with the rotation of the reference system on charged and neutral particles confined by a quantum ring, which is described by the potential of Tan-Inkson. The contribution of the rotation is introduced by its coupling with angular momentum of the system. We show that the rotation is introduced via a non-minimum coupling to the kinetic part of the Hamiltonian describing the quantum dynamics of systems studied here. Thus, we show that non-inertial effects of the rotation induce on the quantum properties of the particles similar effects generated by a magnetic field. We also investigated the contribution of a screw dislocation on the physical properties of the particles. The topological defect contributes as a torsion source, presenting a contribution similar to the Aharonov-Bohm flux. Besides charged particles (electrons and holes), we also study the effects of rotation on neutral particles in three different scenarios: a neutral particle with a permanent magnetic dipole moment coupled by the Aharanov-Casher interaction; a neutral particle with a permanent electric dipole moment coupled by the interaction proposed by He-McKellar-Wilkens and a neutral particle with an electric dipole moment induced by the field configuration proposed by Wei-Han-Wei. In all three cases it is shown the similarity between the neutral and charged particles. We analyze the non-relativistic quantum dynamics of these particles by solving the Schrödinger equation. In addition to the energy spectrum and wave functions, we calculate the persistent current and the magnetization for the four systems studied here, and we also analyzed, from the expression for the persistent current for quantum rings, the limit case for quantum dots.

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.

In this contribution, 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 background. We also study the influence of noninertial effects of a rotating frame and and obtain several contributions to the relativistic geometric phase due to the noninertial effects and the topology of spacetime. The analogous Aharonov-Casher and He-Mckellar-Wilkens effects are investigated in the nonrelativistic dynamics with the presence of a topological defect and under the influence of noninertial effects. We also obtain effects analogous to the Sagnac effect and Mashhoon effect due to the presence of the topological defect.

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 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.

Quantum effects on a neutral particle (atom or molecule) with an induced electric dipole moment are investigated when it is subject to the Kratzer potential and a scalar potential proportional to the radial distance. In addition, this neutral is placed in a region with electric and magnetic fields. This system is analysed in both non-rotating and rotating reference frames. Then, it is shown that bound state solutions to the Schrödinger equation can be achieved and, in the search for polynomial solutions to the radial wave function, a restriction on the values of the cyclotron frequency is analysed in both reference frames.