95 citations · 2.4k across the 176 of their papers we have counts for
43 papers · 1 filter
Polynomial algebras from commutants: Classical and Quantum aspects of
Rutwig Campoamor-Stursberg, Danilo Latini, Ian Marquette +1
We review some aspects of the Racah algebra , including the closure relations, pointing out their role in superintegrability, as well as in the description of the symmetry al…
Polynomial algebras from Lie algebra reduction chains
Rutwig Campoamor-Stursberg, Danilo Latini, Ian Marquette +1
We reexamine different examples of reduction chains of Lie algebras in order to show how the polynomials determining the commutant with respect…
Infinite dimensional representations of cubic and quintic algebras and special functions
Ian Marquette, Junze Zhang, Yao-Zhong Zhang
Finite and Infinite-dimensional representations of symmetry algebras play a significant role in determining the spectral properties of physical Hamiltonians. In this paper, we intr…
Algebraic (super-)integrability from commutants of subalgebras in universal enveloping algebras
Rutwig Campoamor-Stursberg, Danilo Latini, Ian Marquette +1
Starting from a purely algebraic procedure based on the commutant of a subalgebra in the universal enveloping algebra of a given Lie algebra, the notion of algebraic Hamiltonians a…
Construction of polynomial algebras from intermediate Casimir invariants of Lie algebras
Danilo Latini, Ian Marquette, Yao-Zhong Zhang
We propose a systematic procedure to construct polynomial algebras from intermediate Casimir invariants arising from (semisimple or non-semisimple) Lie algebras . In…
Polynomial algebras of superintegrable systems separating in Cartesian coordinates from higher order ladder operators
Danilo Latini, Ian Marquette, Yao-Zhong Zhang
We introduce the general polynomial algebras characterizing a class of higher order superintegrable systems that separate in Cartesian coordinates. The construction relies on under…
-dimensional Smorodinsky-Winternitz model and related higher rank quadratic algebra
Francisco Correa, Md Fazlul Hoque, Ian Marquette +1
The -dimensional Smorodinsky-Winternitz system is a maximally superintegrable and exactly solvable model, being subject of study from different approaches. The model has been de…
Racah Algebra from Coalgebraic Structures and Chains of Substructures
Danilo Latini, Ian Marquette, Yao-Zhong Zhang
The recent interest in the study of higher-rank polynomial algebras related to -dimensional classical and quantum superintegrable systems with coalgebra symmetry and their conne…
Embedding of the Racah Algebra R() and Superintegrability
Danilo Latini, Ian Marquette, Yao-Zhong Zhang
The rank- Racah algebra plays a pivotal role in the theory of superintegrable systems. It appears as the symmetry algebra of the -parameter system on the -sphere fr…
New R-matrices with non-additive spectral parameters and integrable models of strongly correlated fermions
Yao-Zhong Zhang, Jason L. Werry
We present a general formula for constructing R-matrices with non-additive spectral parameters associated with a type-I quantum superalgebra. The spectral parameters originate from…
Superintegrable systems from block separation of variables and unified derivation of their quadratic algebras
Zhe Chen, Ian Marquette, Yao-Zhong Zhang
We present a new method for constructing -dimensional minimally superintegrable systems based on block coordinate separation of variables. We give two new families of superinteg…
Ladder operators and coherent states for multi-step supersymmetric rational extensions of the truncated oscillator
Scott E. Hoffmann, Véronique Hussin, Ian Marquette +1
We construct ladder operators, and , for a multi-step rational extension of the harmonic oscillator on the half plane, . These ladder operator…
Extended Laplace-Runge-Lentz vectors, new family of superintegrable systems and quadratic algebras
Zhe Chen, Ian Marquette, Yao-Zhong Zhang
We present a useful proposition for discovering extended Laplace-Runge-Lentz vectors of certain quantum mechanical systems. We propose a new family of superintegrable systems and c…
Coherent states for ladder operators of general order related to exceptional orthogonal polynomials
Scott E. Hoffmann, Véronique Hussin, Ian Marquette +1
We construct the coherent states of general order, for the ladder operators, and , which act on rational deformations of the harmonic oscillator. The posit…
On superintegrable monopole systems
Md Fazlul Hoque, Ian Marquette, Yao-Zhong Zhang
Superintegrable systems with monopole interactions in flat and curved spaces have attracted much attention. For example, models in spaces with a Taub-NUT metric are well-known to a…
Quantum superintegrable system with a novel chain structure of quadratic algebras
Yidong Liao, Ian Marquette, Yao-Zhong Zhang
We analyse the -dimensional superintegrable Kepler-Coulomb system with non-central terms. We find a novel underlying chain structure of quadratic algebras formed by the integral…
Algebraic calculations for spectrum of superintegrable system from exceptional orthogonal polynomials
Md Fazlul Hoque, Ian Marquette, Sarah Post +1
We introduce an extended Kepler-Coulomb quantum model in spherical coordinates. The Schrödinger equation of this Hamiltonian is solved in these coordinates and it is shown that the…
Non-classical behaviour of coherent states for systems constructed using exceptional orthogonal polynomials
Scott E. Hoffmann, Véronique Hussin, Ian Marquette +1
We construct the coherent states and Schrödinger cat states associated with new types of ladder operators for a particular case of a rationally extended harmonic oscillator involvi…
Quadratic algebra structure in the 5D Kepler system with non-central potentials and Yang-Coulomb monopole interaction
Md Fazlul Hoque, Ian Marquette, Yao-Zhong Zhang
We construct the integrals of motion for the 5D deformed Kepler system with non-central potentials in Yang-Coulomb monopole field. We show that these integrals form a highe…
Recurrence approach and higher rank polynomial algebras for superintegrable monopole systems
Md Fazlul Hoque, Ian Marquette, Yao-Zhong Zhang
We revisit the MIC-harmonic oscillator in flat space with monopole interaction and derive the polynomial algebra satisfied by the integrals of motion and its energy spectrum using…
Quadratic algebra for superintegrable monopole system in a Taub-NUT space
Md Fazlul Hoque, Ian Marquette, Yao-Zhong Zhang
We introduce a Hartmann system in the generalized Taub-NUT space with Abelian monopole interaction. This quantum system includes well known Kaluza-Klein monopole and MIC-Zwanziger…
Recurrence approach and higher rank cubic algebras for the -dimensional superintegrable systems
Md Fazlul Hoque, Ian Marquette, Yao-Zhong Zhang
By applying the recurrence approach and coupling constant metamorphosis, we construct higher order integrals of motion for the Stackel equivalents of the -dimensional superinteg…
Family of -dimensional superintegrable systems and quadratic algebra structures
Md Fazlul Hoque, Ian Marquette, Yao-Zhong Zhang
Classical and quantum superintegrable systems have a long history and they possess more integrals of motion than degrees of freedom. They have many attractive properties, wide appl…
A new family of dimensional superintegrable double singular oscillators and quadratic algebra
Md Fazlul Hoque, Ian Marquette, Yao-Zhong Zhang
We introduce a new family of -dimensional quantum superintegrable model consisting of double singular oscillators of type . The special cases and were p…