14 papers
Generalized quantum Zernike Hamiltonians: Polynomial Higgs-type algebras and algebraic derivation of the spectrum
Rutwig Campoamor-Stursberg, Francisco J. Herranz, Danilo Latini +2
We consider the quantum analog of the generalized Zernike systems given by the Hamiltonian: $$\hat{\mathcal{H}}_N =\hat{p}_1^2+\hat{p}_2^2+\sum_{k=1}^N γ_k (\hat{q}_1 \hat{p}_1+\h…
Contact Lie systems on Riemannian and Lorentzian spaces: from scaling symmetries to curvature-dependent reductions
Rutwig Campoamor-Stursberg, Oscar Carballal, Francisco J. Herranz
We propose an adaptation of the notion of scaling symmetries for the case of Lie-Hamilton systems, allowing their subsequent reduction to contact Lie systems. As an illustration of…
Polynomial Poisson Algebras and Superintegrable Systems from Cartan centralisers of Types , and
Rutwig Campoamor-Stursberg, Danilo Latini, Ian Marquette +2
In this work, we construct explicit formulas for the generators of the Cartan centralisers of complex semisimple Lie algebras and , the case being already know…
Subalgebra chains and nuclear physics: Commutant approach and construction of polynomial algebras
Rutwig Campoamor-Stursberg, Danilo Latini, Ian Marquette +2
In this paper, we review a new approach to study subalgebra chains in the context of nuclear physics. This approach does not rely on explicit r…
Generalized classical and quantum Zernike Hamiltonians
Francisco J. Herranz, Alfonso Blasco, Rutwig Campoamor-Stursberg +3
A superintegrable generalization of the classical and quantum Zernike systems is reviewed. The corresponding Hamiltonians are endowed with higher-order integrals and can be interpr…
Mixed superposition rules for Lie systems and compatible geometric structures
Rutwig Campoamor-Stursberg, Oscar Carballal, Francisco J. Herranz +1
Mixed superposition rules are, in short, a method to describe the general solutions of a time-dependent system of first-order differential equations, a so-called Lie system, in ter…