A comment on the analogous confinement of a neutral particle to a quantum dot via noninertial effects

In this contribution, we discuss the nonrelativistic limit of the Dirac equation for a neutral particle with a permanent electric dipole moment interacting with external fields in a noninertial frame. We show a case where the geometry of the manifold can play the role of a hard-wall confining potential due to noninertial effects, and can yield bound states analogous to a confinement of the spin-half neutral particle interacting with external fields to a quantum dot described by a hard-wall confining potential [33].     

Noninertial Effects on a Dirac Neutral Particle Inducing an Analogue of the Landau Quantization in the Cosmic String Spacetime

We discuss the behavior of external fields interacting with a Dirac neutral particle with a permanent electric dipole moment in order to achieve relativistic bound state solutions in a noninertial frame and in the presence of a topological defect spacetime. We show that the noninertial effects of the Fermi?CWalker reference frame induce a radial magnetic field even in the absence of magnetic charges, which is influenced by the topology of the cosmic string spacetime. We then discuss the conditions that the induced fields must satisfy to yield the relativistic bound states corresponding to the Landau?CHe?CMcKellar?CWilkens quantization in the cosmic string spacetime. Finally, we obtain the Dirac spinors for positive-energy solutions and the Gordon decomposition of the Dirac probability current.     

Relativistic bounds states for a neutral particle confined to a parabolic potential induced by noninertial effects

We obtain the solutions of the Dirac equation when the noninertial effects of the Fermi-Walker reference frame break the relativistic Landau-Aharonov-Casher quantization, but they provide bound states in an analogous way to a Dirac neutral particle subject to Tan-Inkson quantum dot potential [W.-C. Tan, J.C. Inkson, Semicond. Sci. Technol. 11 (1996) 1635].     

Torsion and noninertial effects on a nonrelativistic Dirac particle

We investigate torsion and noninertial effects on a spin-1/2$1/2$ quantum particle in the nonrelativistic limit of the Dirac equation. We consider the cosmic dislocation spacetime as a background and show that a rotating system of reference can be used out to distances which depend on the parameter related to the torsion of the defect. Therefore, we analyse torsion effects on the spectrum of energy of a nonrelativistic Dirac particle confined to a hard-wall potential in a Fermi–Walker reference frame.     

Aharonov–Anandan quantum phases and Landau quantization associated with a magnetic quadrupole moment

The arising of geometric quantum phases in the wave function of a moving particle possessing a magnetic quadrupole moment is investigated. It is shown that an Aharonov–Anandan quantum phase (Aharonov and Anandan, 1987) can be obtained in the quantum dynamics of a moving particle with a magnetic quadrupole moment. In particular, it is obtained as an analogue of the scalar Aharonov–Bohm effect for a neutral particle (Anandan, 1989). Besides, by confining the quantum particle to a hard-wall confining potential, the dependence of the energy levels on the geometric quantum phase is discussed and, as a consequence, persistent currents can arise from this dependence. Finally, an analogue of the Landau quantization is discussed.     

Rotating effects on the Dirac oscillator in the cosmic string spacetime

In this contribution, we study the Dirac oscillator under the influence of noninertial effects of a rotating frame in the cosmic string spacetime. We show that both noninertial effects and the topology of the cosmic string spacetime restrict the physical region of the spacetime where the quantum particle can be placed, and discuss two different cases of bound states solutions of the Dirac equation by analysing the behaviour of the Dirac oscillator frequency.     

二维荷电粒子维格纳晶格:边界效应

采用一种非线性的优化方法,研究了处于硬壁限制势下二维带电多粒子系统的基态,分析不同形状边界对系统基态构型的影响.由于圆形边界对称性高,基态结构和抛物限制势下情况相似.在正方形边界下,当系统粒子数N<66时,荷电粒子形成方形晶格;当N≥66时,由于边界影响被削弱,内层粒子形成六角维格纳晶格.进一步分析了椭圆和矩形边界对维格纳晶格的影响.     

Comparing the reliability of networks by spectral analysis

Topological effects on the confinement of a moving neutral particle with an induced electric dipole moment confined to a quantum ring and a two-dimensional quantum dot (described by a hard-wall confining potential) are investigated. It is shown in this work that the spectrum of energy depends on the geometric phase obtained by Wei et al. [H. Wei, R. Han, X. Wei, Phys. Rev. Lett. 75, 2071 (1995)] and persistent currents arise from this dependence in both the quantum ring and the quantum dot. Further, the behaviour of the analogue of the Landau system for a moving electric dipole confined to a two-dimensional quantum dot is discussed, and it is shown that persistent currents are absent in this case.     

Scalar bosons under the influence of noninertial effects in the cosmic string spacetime

In this paper we present two different classes of solutions for the Klein–Gordon equation in the presence of a scalar potential under the influence of noninertial effects in the cosmic string spacetime. We show that noninertial effects restrict the physical region of the spacetime where the particle can be placed, and furthermore that the energy levels are shifted by these effects. In addition, we show that the presence of a Coulomb-like scalar potential allows the formation of bound states when the Klein–Gordon equation is considered in this kind of spacetime.     

On a relativistic scalar particle subject to a Coulomb-type potential given by Lorentz symmetry breaking effects

The behaviour of a relativistic scalar particle in a possible scenario that arises from the violation of the Lorentz symmetry is investigated. The background of the Lorentz symmetry violation is defined by a tensor field that governs the Lorentz symmetry violation out of the Standard Model Extension. Thereby, we show that a Coulomb-type potential can be induced by Lorentz symmetry breaking effects and bound states solutions to the Klein–Gordon equation can be obtained. Further, we discuss the effects of this Coulomb-type potential on the confinement of the relativistic scalar particle to a linear confining potential by showing that bound states solutions to the Klein–Gordon equation can also be achieved, and obtain a quantum effect characterized by the dependence of a parameter of the linear confining potential on the quantum numbers {n,l}$\{n,l\}$ of the system.     

Aharonov-Casher effect and persistent spin currents in a Coulomb-type potential induced by Lorentz symmetry breaking effects

We investigate quantum effects on a nonrelativistic neutral particle with a permanent magnetic dipole moment that interacts with an electric field. This neutral particle is also under the influence of a background that breaks the Lorentz symmetry. We focus on the Lorentz symmetry violation background determined by a space-like vector field. Then, we show that the effects of the violation of Lorentz symmetry can yield an attractive Coulomb-type potential. Furthermore, we obtain the bound state solutions to the Schrödinger-Pauli equation and show that the spectrum of energy is a function of the Aharonov-Casher geometric quantum phase. Finally, we discuss the arising of persistent spin currents.     

Relativistic Landau–He–McKellar–Wilkens quantization and relativistic bound states solutions for a Coulomb-like potential induced by the Lorentz symmetry breaking effects

In this work, we discuss the relativistic Landau–He–McKellar–Wilkens quantization and relativistic bound states solutions for a Dirac neutral particle under the influence of a Coulomb-like potential induced by the Lorentz symmetry breaking effects. We present new possible scenarios of studying Lorentz symmetry breaking effects by fixing the space-like vector field background in special configurations. It is worth mentioning that the criterion for studying the violation of Lorentz symmetry is preserving the gauge symmetry.     

Induced electric dipole in a quantum ring

In this contribution, we investigate the quantum dynamics of a neutral particle confined in a quantum ring potential. We use two different field configurations for induced electric dipole in the presence of electric and magnetic fields and a general confining potential, for which we solve the Schrödinger equation and obtain the complete set of eigenfunctions and eigenvalues.     

Effective field theory for bound state reflection

Elastic quantum bound-state reflection from a hard-wall boundary provides direct information regarding the structure and compressibility of quantum bound states. We discuss elastic quantum bound-state reflection and derive a general theory for elastic reflection of shallow dimers from hard-wall surfaces using effective field theory. We show that there is a small expansion parameter for analytic calculations of the reflection scattering length. We present a calculation up to second order in the effective Hamiltonian in one, two, and three dimensions. We also provide numerical lattice results for all three cases as a comparison with our effective field theory results. Finally, we provide an analysis of the compressibility of the alpha particle confined to a cubic lattice with vanishing Dirichlet boundaries.     

Spin edge helices in a perpendicular magnetic field

We present an exact solution to the problem of the spin edge states in the presence of equal Bychkov-Rashba and Dresselhaus spin-orbit fields in a two-dimensional electron system, restricted by a hard-wall confining potential and exposed to a perpendicular magnetic field. We find that the spectrum of the spin edge states depends critically on the orientation of the sample edges with respect to the crystallographic axes. Such a strikingly different spectral behavior generates new modes of the persistent spin helix-spin edge helices with novel properties, which can be tuned by the applied electric and magnetic fields.     

Deconfinement transition: a three dimensional model

We present a three–dimensional model for quark matter with a density dependent quark–quark (confining) potential, which allows to describe a sort of deconfinement transition as the system evolves from a low density assembly of bound structures to a high density free Fermi gas of quarks. We consider different confining potentials, some of which successfully utilized in hadron spectroscopy. We find that a proper treatment of the many–body correlations induced by the medium is essential to disentangle the different nature of the two (hadronic and deconfined) phases of the system. For this purpose the ground state energy per particle and the pair correlation function are investigated. Received: 10 June 1998 / Revised version: 24 September 1998     

On the Effects of Curvature on the Confinement of a Neutral Particle to a Quantum Dot Induced by Non-inertial Effects

We discuss the influence of a linear topological defect on the bound states of a non-relativistic neutral particle with permanent magnetic dipole moment in two distinct cases: In the first case, we consider a Fermi-Walker reference frame for the observers and show how non-inertial effects yield bound states analogous to having a neutral particle subject to the Tan-Inkson model for a quantum dot (W.-C. Tan, J.C. Inkson, Semicond. Sci. Technol. 11:1635, 1996); in the second case, we consider the action of a constant force and obtain the energy levels of the bound states.     

Bound States in Curved Quantum Layers

We consider a nonrelativistic quantum particle constrained to a curved layer of constant width built over a non-compact surface embedded in ℝ³. We suppose that the latter is endowed with the geodesic polar coordinates and that the layer has the hard-wall boundary. Under the assumption that the surface curvatures vanish at infinity we find sufficient conditions which guarantee the existence of geometrically induced bound states. Received: 26 February 2001 / Accepted: 21 May 2001     

Rashba coupling in three-electron-quantum dot: A numerical solution

We present a numerical solution of a Schrödinger equation for three electrons in a quantum dot with hard-wall confining potential in the presence Spin-Orbit coupling. After separation of the problem by some hyperspherical technique, we have solved the resulting equations by using a novel finite difference method. Then a study of the wave functions, eigen-energies and accuracy of the method is done.     

On the harmonic-type and linear-type confinement of a relativistic scalar particle yielded by Lorentz symmetry breaking effects

Based on the Standard Model Extension, we investigate relativistic quantum effects on a scalar particle in backgrounds of the Lorentz symmetry violation defined by a tensor field. We show that harmonic-type and linear-type confining potentials can stem from Lorentz symmetry breaking effects, and thus, relativistic bound state solutions can be achieved. We first analyse a possible scenario of the violation of the Lorentz symmetry that gives rise to a harmonic-type potential. In the following, we analyse another possible scenario of the breaking of the Lorentz symmetry that induces both harmonic-type and linear-type confining potentials. In this second case, we also show that not all values of the parameter associated with the intensity of the electric field are permitted in the search for polynomial solutions to the radial equation, where the possible values of this parameter are determined by the quantum numbers of the system and the parameters associated with the violation of the Lorentz symmetry.