scholarly journals Degeneration of the Superintegrable System with Potentials Described by the Sixth Painlevé Transcendents

2014 ◽  
Vol 02 (11) ◽  
pp. 996-999
Author(s):  
Yoshikatsu Sasaki
Keyword(s):  
Superintegrable System

scholarly journals Carter's constant and superintegrability

2018 ◽  
Vol 27 (07) ◽  
pp. 1850066
Author(s):  
Payel Mukhopadhyay ◽  
K. Rajesh Nayak
Keyword(s):  
Dynamical System ◽  
Degrees Of Freedom ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Integrals Of Motion ◽  
Superintegrable System ◽  
Simple Observation ◽  
Superintegrable Systems ◽  
Axisymmetric Spacetime ◽  
Three Degrees Of Freedom

Carter's constant is a nontrivial conserved quantity of motion of a particle moving in stationary axisymmetric spacetime. In the version of the theorem originally given by Carter, due to the presence of two Killing vectors, the system effectively has two degrees of freedom. We propose an extension to the first version of Carter's theorem to a system having three degrees of freedom to find two functionally independent Carter-like integrals of motion. We further generalize the theorem to a dynamical system with [Formula: see text] degrees of freedom. We further study the implications of Carter's constant to superintegrability and present a different approach to probe a superintegrable system. Our formalism gives another viewpoint to a superintegrable system using the simple observation of separable Hamiltonian according to Carter's criteria. We then give some examples by constructing some two-dimensional superintegrable systems based on this idea and also show that all three-dimensional simple classical superintegrable potentials are also Carter separable.

scholarly journals Algebraic calculations for spectrum of superintegrable system from exceptional orthogonal polynomials

2018 ◽  
Vol 391 ◽  
pp. 203-215 ◽  
Author(s):  
Md. Fazlul Hoque ◽  
Ian Marquette ◽  
Sarah Post ◽  
Yao-Zhong Zhang
Keyword(s):  
Orthogonal Polynomials ◽  
Superintegrable System ◽  
Exceptional Orthogonal Polynomials

Superintegrable system on a sphere with the integral of higher degree

2009 ◽  
Vol 14 (6) ◽  
pp. 615-620 ◽  
Author(s):  
A. V. Borisov ◽  
A. A. Kilin ◽  
I. S. Mamaev
Keyword(s):  
Superintegrable System

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 maximally superintegrable system on an -dimensional space of nonconstant curvature

2008 ◽  
Vol 237 (4) ◽  
pp. 505-509 ◽  
Author(s):  
Á. Ballesteros ◽  
A. Enciso ◽  
F.J. Herranz ◽  
O. Ragnisco
Keyword(s):  
Dimensional Space ◽  
Superintegrable System

scholarly journals Stäckel Equivalence of Non-Degenerate Superintegrable Systems, and Invariant Quadrics

2021 ◽  
Author(s):  
Andreas Vollmer ◽  
Keyword(s):  
Equivalence Class ◽  
Second Order ◽  
Coupling Constant ◽  
Superintegrable System ◽  
Superintegrable Systems ◽  
Dimension 2

A non-degenerate second-order maximally conformally superintegrable system in dimension 2 naturally gives rise to a quadric with position dependent coefficients. It is shown how the system's Stäckel class can be obtained from this associated quadric.The Stäckel class of a second-order maximally conformally superintegrable system is its equivalence class under Stäckel transformations, i.e., under coupling-constant metamorphosis.

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