Searcharxiv⌕ Search

arXiv subjects

R. D. Mota

Publications and source records attributed to R. D. Mota.

35 records · Page 2Linked to original sources
arXiv2016

$SU(1,1)$ solution for the Dunkl-Coulomb problem in two dimensions and its coherent states

We study the radial part of the Dunkl-Coulomb problem in two dimensions and show that this problem possesses the $su(1,1)$ symmetry. We introduce two different realizations for the $su(1,1)$ Lie algebra and use the theory of irreducible representations to obtain the energy spectrum and the eigenfunctions. For the first algebra realization, we apply the Schrödinger factorization to the radial part of the Dunkl-Coulomb problem to construct the algebra generators. In the second realization, we introduce three operators, been one of them proportional to the radial Hamiltonian. Finally, we use the $su(1,1)$ Sturmian basis of one of the two algebras to construct the radial coherent states in a closed form.

math-ph↗
arXiv2016

$SU(1,1)$ solution for the Dunkl oscillator in two dimensions and its coherent states

We study the Dunkl oscillator in two dimensions by the $su(1,1)$ algebraic method. We apply the Schrödinger factorization to the radial Hamiltonian of the Dunkl oscillator to find the $su(1,1)$ Lie algebra generators. The energy spectrum is found by using the theory of unitary irreducible representations. By solving analytically the Schrödinger equation, we construct the Sturmian basis for the unitary irreducible representations of the $su(1,1)$ Lie algebra. We construct the $SU(1,1)$ Perelomov radial coherent states for this problem and compute their time evolution.

math-ph↗
arXiv2016

$SU(1,1)$ Approach to Stokes Parameters and the Theory of Light Polarization

We introduce an alternative approach to the polarization theory of light. This is based on a set of quantum operators, constructed from two independent bosons, being three of them the $su(1,1)$ Lie algebra generators, and the other one, the Casimir operator of this algebra. By taking the expectation value of these generators in a two-mode coherent state, their classical limit is obtained. We use these classical quantities to define the new Stokes-like parameters. We show that the light polarization ellipse can be written in terms of the Stokes-like parameters. Also, we write these parameters in terms of other two quantities, and show that they define a one-sheet (Poincaré hyperboloid) of a two-sheet hyperboloid. Our study is restricted to the case of a monochromatic plane electromagnetic wave which propagates along the $z$ axis.

quant-ph↗
arXiv2016

A generalized Jaynes-Cummings model: The relativistic parametric amplifier and a single trapped ion

We introduce a generalization of the Jaynes-Cummings model and study some of its properties. We obtain the energy spectrum and eigenfunctions of this model by using the tilting transformation and the squeezed number states of the one-dimensional har- monic oscillator. As physical applications, we connect this new model to two important and novelty problems: the relativistic parametric amplifier and the quantum simulation of a single trapped ion.

hep-th↗
arXiv2016

Algebraic approach and coherent states for a relativistic quantum particle in cosmic string spacetime

We study a relativistic quantum particle in cosmic string spacetime in the presence of a uniform magnetic field and a Coulomb-type scalar potential. It is shown that the radial part of this problem possesses the $su(1,1)$ symmetry. We obtain the energy spectrum and eigenfunctions of this problem by using two algebraic methods: the Schrödinger factorization and the tilting transformation. Finally, we give the explicit form of the relativistic coherent states for this problem.

quant-ph↗
arXiv2015

The number radial coherent states for the generalized MICZ-Kepler problem

We study the radial part of the MICZ-Kepler problem in an algebraic way by using the $su(1,1)$ Lie algebra. We obtain the energy spectrum and the eigenfunctions of this problem from the $su(1,1)$ theory of unitary representations and the tilting transformation to the stationary Schrödinger equation. We construct the physical Perelomov number coherent states for this problem and compute some expectation values. Also, we obtain the time evolution of these coherent states.

math-ph↗
arXiv2014

Coherent states for the two-dimensional Dirac-Moshinsky oscillator coupled to an external magnetic field

We show that the $(2+1)$-dimensional Dirac-Moshinsky oscillator coupled to an external magnetic field can be treated algebraically with the $SU(1,1)$ group theory and its group basis. We use the $su(1,1)$ irreducible representation theory to find the energy spectrum and the eigenfunctions. Also, with the $su(1,1)$ group basis we construct the relativistic coherent states in a closed form for this problem.

hep-th↗
arXiv2013

The SU(1,1) Perelomov number coherent states and the non-degenerate parametric amplifier

We construct the Perelomov number coherent states for any three $su(1,1)$ Lie algebra generators and study some of their properties. We introduce three operators which act on Perelomov number coherent states and close the $su(1,1)$ Lie algebra. We show that the most general $SU(1,1)$ coherence-preserving Hamiltonian has the Perelomov number coherent states as eigenfunctions, and we obtain their time evolution. We apply our results to obtain the non-degenerate parametric amplifier eigenfunctions, which are shown to be the Perelomov number coherent states of the two-dimensional harmonic oscillator.

math-ph↗
arXiv2013

$SU(1,1)$ coherent states for Dirac-Kepler-Coulomb problem in $D+1$ dimensions with scalar and vector potentials

We decouple the Dirac's radial equations in $D+1$ dimensions with Coulomb-type scalar and vector potentials through appropriate transformations. We study each of these uncoupled second-order equations in an algebraic way by using an $su(1,1)$ algebra realization. Based on the theory of irreducible representations, we find the energy spectrum and the radial eigenfunctions. We construct the Perelomov coherent states for the Sturmian basis, which is the basis for the unitary irreducible representation of the $su(1,1)$ Lie algebra. The physical radial coherent states for our problem are obtained by applying the inverse original transformations to the Sturmian coherent states.

math-ph↗
arXiv2011

su(1,1) Algebraic approach of the Dirac equation with Coulomb-type scalar and vector potentials in D + 1 dimensions

We study the Dirac equation with Coulomb-type vector and scalar potentials in D + 1 dimensions from an su(1, 1) algebraic approach. The generators of this algebra are constructed by using the Schrödinger factorization. The theory of unitary representations for the su(1, 1) Lie algebra allows us to obtain the energy spectrum and the supersymmetric ground state. For the cases where there exists either scalar or vector potential our results are reduced to those obtained by analytical techniques.

hep-th↗
arXiv2010

An $su(1,1)$ algebraic approach for the relativistic Kepler-Coulomb problem

We apply the Schrödinger factorization method to the radial second-order equation for the relativistic Kepler-Coulomb problem. From these operators we construct two sets of one-variable radial operators which are realizations for the $su(1,1)$ Lie algebra. We use this algebraic structure to obtain the energy spectrum and the supersymmetric ground state for this system.

math-ph↗
arXiv2010

The su(1,1) dynamical algebra from the Schrödinger ladder operators for N-dimensional systems: hydrogen atom, Mie-type potential, harmonic oscillator and pseudo-harmonic oscillator

We apply the Schrödinger factorization to construct the ladder operators for hydrogen atom, Mie-type potential, harmonic oscillator and pseudo-harmonic oscillator in arbitrary dimensions. By generalizing these operators we show that the dynamical algebra for these problems is the $su(1,1)$ Lie algebra.

quant-ph↗
arXiv2008

Jordan-Schwinger map, 3D harmonic oscillator constants of motion, and classical and quantum parameters characterizing electromagnetic wave polarization

In this work we introduce a generalization of the Jauch and Rohrlich quantum Stokes operators when the arrival direction from the source is unknown {\it a priori}. We define the generalized Stokes operators as the Jordan-Schwinger map of a triplet of harmonic oscillators with the Gell-Mann and Ne'eman SU(3) symmetry group matrices. We show that the elements of the Jordan-Schwinger map are the constants of motion of the three-dimensional isotropic harmonic oscillator. Also, we show that generalized Stokes Operators together with the Gell-Mann and Ne'eman matrices may be used to expand the polarization density matrix. By taking the expectation value of the Stokes operators in a three-mode coherent state of the electromagnetic field, we obtain the corresponding generalized classical Stokes parameters. Finally, by means of the constants of motion of the classical three-dimensional isotropic harmonic oscillator we describe the geometric properties of the polarization ellipse

math-ph↗
arXiv2001

Nonlocal calculation for nonstrange dibaryons and tribaryons

We study the possible existence of nonstrange dibaryons and tribaryons by solving the bound-state problem of the two- and three-body systems composed of nucleons and deltas. The two-body systems are $NN$, $NΔ$, and $ΔΔ$, while the three-body systems are $NNN$, $NNΔ$, $NΔΔ$, and $ΔΔΔ$. We use as input the nonlocal $NN$, $NΔ$, and $ΔΔ$ potentials derived from the chiral quark cluster model by means of the resonating group method. We compare with previous results obtained from the local version based on the Born-Oppenheimer approximation.

nucl-th↗