Dynamical and structural symmetries for the highest Landau levels on the AdS 2

Open Physics ◽  
2012 ◽  
Vol 10 (2) ◽  
Author(s):  
Pakhshan Espoukeh ◽  
Hossein Fakhri
Keyword(s):  
Magnetic Field ◽  
Differential Operators ◽  
Dynamical Symmetry ◽  
Quantization Condition ◽  
Landau Levels ◽  
Irreducible Representations ◽  
Legendre Functions ◽  
Ladder Operators ◽  
Associated Legendre Functions ◽  
Dirac Quantization

AbstractThe aim of the paper is to use the recurrence relations with respect to both indices of the associated Legendre functions for the extraction of the Dirac quantization condition and dynamical symmetry group U(1, 1) corresponding to the highest Landau levels on the hyperbolic plane with uniform magnetic field B. Irreducible representations of the su(2) algebra are obtained by the ladder differential operators which change B by 1/2 unit and mode number by one unit. Two different classes of the irreducible representations of SU(1, 1) with the even and odd boson numbers 2B − 1/2 are extracted for the Bargmann indices 1/4 and 3/4, respectively. Finally, we show that shape invariance symmetry is realized by the ladder operators which shift only the magnetic field B by 1/2 unit.

PARASUPERSYMMETRIC COHERENT STATES FOR LANDAU LEVELS WITH DYNAMICAL SYMMETRY GROUP H4

2002 ◽  
Vol 17 (28) ◽  
pp. 4081-4093 ◽  
Author(s):  
H. FAKHRI ◽  
H. MOTAVALI
Keyword(s):  
Magnetic Field ◽  
Symmetry Group ◽  
Coherent States ◽  
Ad Hoc ◽  
Flat Surface ◽  
Arbitrary Order ◽  
Dynamical Symmetry ◽  
Quantum States ◽  
Landau Levels ◽  
Lowering Operator

The eigenstates and their degeneracy for parasupersymmetric Hamiltonian of arbitrary order p, corresponding to the motion of a charged particle with spin [Formula: see text] on the flat surface in the presence of a constant magnetic field along z-axis, are calculated. The eigenstates are expressed in terms of Landau levels quantum states with dynamical symmetry group H4. Furthermore, parasupersymmetric coherent states with multiplicity degeneracy are derived for an ad hoc lowering operator of the eigenstates in terms of ordinary coherent states of Landau Hamiltonian.

BARUT–GIRARDELLO COHERENT STATES CONSTRUCTED BY Ym m(θ,φ) AND Ym+1 m(θ,φ) FOR A FREE PARTICLE ON THE SPHERE

2004 ◽  
Vol 19 (35) ◽  
pp. 2619-2628 ◽  
Author(s):  
A. CHENAGHLOU ◽  
H. FAKHRI
Keyword(s):  
Lie Algebra ◽  
Coherent States ◽  
Free Particle ◽  
Irreducible Representations ◽  
Legendre Functions ◽  
Associated Legendre Functions ◽  
Shape Invariance ◽  
Infinite Dimensional ◽  
Direct Sum ◽  
Lowering Operator

Using the realization idea of simultaneous shape invariance with respect to two different parameters of the associated Legendre functions, the Hilbert space of spherical harmonics Yn m(θ,φ) corresponding to the motion of a free particle on a sphere is split into a direct sum of infinite-dimensional Hilbert subspaces. It is shown that these Hilbert subspaces constitute irreducible representations for the Lie algebra u (1,1). Then by applying the lowering operator of the Lie algebra u (1,1), Barut–Girardello coherent states are constructed for the Hilbert subspaces consisting of Ym m(θ,φ) and Ym+1 m(θ,φ).

scholarly journals Landau Levels in a Gravitational Field: The Schwarzschild Spacetime Case

Universe ◽  
2021 ◽  
Vol 7 (5) ◽  
pp. 144
Author(s):  
Alexandre Landry ◽  
Fayçal Hammad
Keyword(s):  
Magnetic Field ◽  
Differential Equation ◽  
Gravitational Field ◽  
Power Law ◽  
Quantum Particle ◽  
Energy Levels ◽  
Gravitational Effect ◽  
Quantization Condition ◽  
Landau Levels ◽  
Relativistic Regime

We investigate the gravitational effect on Landau levels. We show that the familiar infinite Landau degeneracy of the energy levels of a quantum particle moving inside a uniform and constant magnetic field is removed by the interaction of the particle with a gravitational field. Two independent approaches are used to solve the relevant Schrödinger equation within the Newtonian approximation. It is found that both approaches yield qualitatively similar results within their respective approximations. With the goal of clarifying some results found in the literature concerning the use of a third independent approach for extracting the quantization condition based on a similar differential equation, we show that such an approach cannot yield a general and yet consistent result. We point out to the more accurate, but impractical, way to use such an approach; a way which does in principle yield a consistent quantization condition. We discuss how our results could be used to contribute in a novel way to the existing methods for testing gravity at the tabletop experiments level as well as at the astrophysical observational level by deriving the corrections brought by Yukawa-like and power-law deviations from the inverse-square law. The full relativistic regime is also examined in detail.

MATHEMATICAL MODELING OF TEMPERATURE EFFECT ON THE FAN CHART OF MAGNETOABSORPTION SPECTRUM IN SEMICONDUCTORS

2019 ◽  
pp. 104-115
Author(s):  
G. Gulyamov ◽  
U. I. Erkaboev ◽  
A. G. Gulyamov
Keyword(s):  
Mathematical Modeling ◽  
Magnetic Field ◽  
Temperature Dependence ◽  
Density Of States ◽  
Landau Levels ◽  
Joint Density ◽  
Narrow Gap ◽  
Narrow Gap Semiconductors ◽  
Dispersion Law ◽  
The Magnetic Field

The article considers the oscillations of interband magneto-optical absorption in semiconductors with the Kane dispersion law. We have compared the changes in oscillations of the joint density of states with respect to the photon energy for different Landau levels in parabolic and non-parabolic zones. An analytical expression is obtained for the oscillation of the combined density of states in narrow-gap semiconductors. We have calculated the dependence of the maximum photon energy on the magnetic field at different temperatures. A theoretical study of the band structure showed that the magnetoabsorption oscillations decrease with an increase in temperature, and the photon energies nonlinearly depend on a strong magnetic field. The article proposes a simple method for calculating the oscillation of joint density of states in a quantizing magnetic field with the non-quadratic dispersion law. The temperature dependence of the oscillations joint density of states in semiconductors with non-parabolic dispersion law is obtained. Moreover, the article studies the temperature dependence of the band gap in a strong magnetic field with the non-quadratic dispersion law. The method is applied to the research of the magnetic absorption in narrow-gap semiconductors with nonparabolic dispersion law. It is shown that as the temperature increases, Landau levels are washed away due to thermal broadening and density of states turns into a density of states without a magnetic field. Using the mathematical model, the temperature dependence of the density distribution of energy states in strong magnetic fields is considered. It is shown that the continuous spectrum of the density of states, measured at the temperature of liquid nitrogen, at low temperatures turns into discrete Landau levels. Mathematical modeling of processes using experimental values of the continuous spectrum of the density of states makes it possible to calculate discrete Landau levels. We have created the three-dimensional fan chart of magneto optical oscillations of semiconductors with considering for the joint density of energy states. For a nonquadratic dispersion law, the maximum frequency of the absorbed light and the width of the forbidden band are shown to depend nonlinearly on the magnetic field. Modeling the temperature  dependence allowed us to determine the Landau levels in semiconductors in a wide temperature spectrum. Using the proposed model, the experimental results obtained for narrow-gap semiconductors are analyzed. The theoretical results are compared with experimental results.

Algebraic structure of Dirac–Pauli equation with account to AMM of neutron in the presence of magnetic field with cylindrical symmetry

2021 ◽  
pp. 2150121
Author(s):  
Masoud Seidi
Keyword(s):  
Magnetic Field ◽  
Lie Algebra ◽  
Algebraic Structure ◽  
Anomalous Magnetic Moment ◽  
Casimir Operator ◽  
Cylindrical Symmetry ◽  
Pauli Equation ◽  
Eigenvalues And Eigenfunctions ◽  
Ladder Operators ◽  
Nu Method

The eigenvalues and eigenfunctions of Dirac–Pauli equation have been obtained for a neutron with anomalous magnetic moment (AMM) in the presence of a strong magnetic field with cylindrical symmetry. In our calculations, the Nikiforov and Uvarov (NU) method has been used. Using the eigenfunctions and construction of the ladder operators, we show that these generators satisfy su(2) Lie algebra and computed the second-order Casimir operator of the lie algebra.

scholarly journals Derivatives of addition theorems for Legendre functions

1995 ◽  
Vol 37 (2) ◽  
pp. 212-234 ◽  
Author(s):  
D.E. Winch ◽  
P.H. Roberts
Keyword(s):  
Spherical Harmonics ◽  
Chebyshev Polynomials ◽  
Legendre Polynomials ◽  
Addition Theorem ◽  
Legendre Functions ◽  
Addition Theorems ◽  
Associated Legendre Functions ◽  
Tensor Spherical Harmonics ◽  
Derivatives Of

AbstractDifferentiation of the well-known addition theorem for Legendre polynomials produces results for sums over order m of products of various derivatives of associated Legendre functions. The same method is applied to the corresponding addition theorems for vector and tensor spherical harmonics. Results are also given for Chebyshev polynomials of the second kind, corresponding to ‘spin-weighted’ associated Legendre functions, as used in studies of distributions of rotations.

scholarly journals Spatially Restricted Integrals in Gradiometric Boundary Value Problems

2009 ◽  
Vol 44 (4) ◽  
pp. 131-148 ◽  
Author(s):  
M. Eshagh
Keyword(s):  
Boundary Value Problems ◽  
Boundary Value ◽  
Legendre Functions ◽  
Gravity Gradiometry ◽  
Satellite Gravity Gradiometry ◽  
Satellite Gravity ◽  
Earth’S Gravity Field ◽  
Associated Legendre Functions ◽  
Tensor Spherical Harmonics ◽  
Slepian Functions

Spatially Restricted Integrals in Gradiometric Boundary Value ProblemsThe spherical Slepian functions can be used to localize the solutions of the gradiometric boundary value problems on a sphere. These functions involve spatially restricted integral products of scalar, vector and tensor spherical harmonics. This paper formulates these integrals in terms of combinations of the Gaunt coefficients and integrals of associated Legendre functions. The presented formulas for these integrals are useful in recovering the Earth's gravity field locally from the satellite gravity gradiometry data.

LANDAU LEVELS AND VERTEX OPERATIONS FOR ANYONS

1991 ◽  
Vol 06 (30) ◽  
pp. 2819-2826 ◽  
Author(s):  
GERALD V. DUNNE ◽  
ALBERTO LERDA ◽  
CARLO A. TRUGENBERGER
Keyword(s):  
Magnetic Field ◽  
Angular Momentum ◽  
External Magnetic Field ◽  
String Theory ◽  
Ground State ◽  
Correlation Functions ◽  
Landau Levels ◽  
Vertex Operators ◽  
Many Body

We construct exact many-body eigenstates of both energy and angular momentum for the N-anyon problem in an external magnetic field. We show that such states span the full ground state eigenspace and arise as correlation functions of Fubini-Veneziano vertex operators of string theory.

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