scholarly journals Superintegrability of the caged anisotropic oscillator

2008 ◽  
Vol 49 (9) ◽  
pp. 092902 ◽  
Author(s):  
N. W. Evans ◽  
P. E. Verrier
Keyword(s):  
Anisotropic Oscillator

Dirac equation with anisotropic oscillator, quantum E3′ and Holt superintegrable potentials and relativistic generalized Yang–Coulomb monopole system

2016 ◽  
Vol 14 (01) ◽  
pp. 1750004 ◽  
Author(s):  
Vahid Mohammadi ◽  
Alireza Chenaghlou
Keyword(s):  
Dirac Equation ◽  
Relativistic Energy ◽  
Integrals Of Motion ◽  
Superintegrable System ◽  
Energy Eigenvalues ◽  
System A ◽  
Superintegrable Systems ◽  
Casimir Operators ◽  
Oscillator Quantum ◽  
Anisotropic Oscillator

The two-dimensional Dirac equation with spin and pseudo-spin symmetries is investigated in the presence of the maximally superintegrable potentials. The integrals of motion and the quadratic algebras of the superintegrable quantum [Formula: see text], anisotropic oscillator and the Holt potentials are studied. The corresponding Casimir operators and the structure functions of the mentioned superintegrable systems are found. Also, we obtain the relativistic energy spectra of the corresponding superintegrable systems. Finally, the relativistic energy eigenvalues of the generalized Yang–Coulomb monopole (YCM) superintegrable system (a [Formula: see text] non-Abelian monopole) are calculated by the energy spectrum of the eight-dimensional oscillator which is dual to the former system by Hurwitz transformation.

scholarly journals A new integrable anisotropic oscillator on the two-dimensional sphere and the hyperbolic plane

2014 ◽  
Vol 47 (34) ◽  
pp. 345204 ◽  
Author(s):  
Ángel Ballesteros ◽  
Alfonso Blasco ◽  
Francisco J Herranz ◽  
Fabio Musso
Keyword(s):  
Hyperbolic Plane ◽  
Dimensional Sphere ◽  
Two Dimensional ◽  
Anisotropic Oscillator

KELVIN CIRCULATION IN A CRANKED ANISOTROPIC OSCILLATOR + BCS MEAN FIELD

1994 ◽  
Vol 03 (04) ◽  
pp. 1251-1266 ◽  
Author(s):  
G. ROSENSTEEL ◽  
A.L. GOODMAN
Keyword(s):  
Phase Transitions ◽  
Mean Field ◽  
Critical Values ◽  
Rigid Rotor ◽  
Expectation Value ◽  
Flow Limit ◽  
Nuclear Rotation ◽  
Deformed Nucleus ◽  
Pairing Field ◽  
Anisotropic Oscillator

The Kelvin circulation vector is the hermitian kinematical observable that measures the true character of nuclear rotation. For a rotating deformed nucleus modeled by a selfconsistent cranked anisotropic oscillator mean field with BCS pairing, the expectation value of the Kelvin circulation operator depends upon the deformation and upon the strength of the pairing field. For zero pairing, the circulation acquires its rigid rotor value. As the pairing field increases, the circulation tends to zero, the irrotational flow limit. At critical values of the pairing field, the deformation and circulation make abrupt phase transitions.

Many-particle states of the anisotropic oscillator

1974 ◽  
Vol 10 (2) ◽  
pp. 901-908
Author(s):  
J. P. Draayer ◽  
S. A. Williams
Keyword(s):  
Anisotropic Oscillator

A generalized statistical complexity based on Rényi entropy of a noncommutative anisotropic oscillator in a homogeneous magnetic field

2019 ◽  
Vol 34 (20) ◽  
pp. 1950105 ◽  
Author(s):  
Debraj Nath ◽  
Piu Ghosh
Keyword(s):  
Magnetic Field ◽  
Homogeneous Magnetic Field ◽  
Renyi Entropy ◽  
Rényi Entropy ◽  
Monotone Functions ◽  
Statistical Complexity ◽  
The Magnetic Field ◽  
Anisotropic Oscillator ◽  
Do So ◽  
Noncommutative Parameter

We calculate the shape Rényi and generalized Rényi complexity of a noncommutative anisotropic harmonic oscillator in a homogeneous magnetic field. To do so, we first obtain the Rényi entropy in position and momentum spaces of the exact normalized wave functions. We observe that shape Rényi and generalized Rényi complexities are monotone functions of noncommutative parameter ([Formula: see text]) in some short range in position space. We analyze the effect of the noncommutative parameter, the magnetic field and the anisotropy on shape Rényi and generalized Rényi complexities.

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