Painlevé VI superintegrability and Heun-Racah algebras
https://arxiv.org/pdf/2611.00322
Ian Marquette, Sarah Post.
https://arxiv.org/pdf/2611.00322
Ian Marquette, Sarah Post.
https://arxiv.org/abs/2611.00322
arXiv abstract link
arxiv.org
November 4, 2026 at 5:42 AM
Painlevé VI superintegrability and Heun-Racah algebras
https://arxiv.org/pdf/2611.00322
Ian Marquette, Sarah Post.
https://arxiv.org/pdf/2611.00322
Ian Marquette, Sarah Post.
Develops three complementary algebraic descriptions of 3D superintegrable quantum systems in magnetic fields using quadratic algebras, deformed-oscillator representations, and sl(2)/sl(3) Sturm algebraization to expose hidden symmetries.
#QuantumAlgebra #Superintegrability #Research
#QuantumAlgebra #Superintegrability #Research
Quadratic Symmetry Algebras and Sturm Algebraization of Superintegrable Magnetic Systems
iq.fp2.dev
November 1, 2026 at 5:06 PM
Develops three complementary algebraic descriptions of 3D superintegrable quantum systems in magnetic fields using quadratic algebras, deformed-oscillator representations, and sl(2)/sl(3) Sturm algebraization to expose hidden symmetries.
#QuantumAlgebra #Superintegrability #Research
#QuantumAlgebra #Superintegrability #Research
Using polynomial algebra and deformed-oscillator methods, researchers derived the exact spectrum and complete representations for a three-dimensional oscillator with two coupled spin-1/2 particles.
#QuantumAlgebra #Superintegrability #Research
#QuantumAlgebra #Superintegrability #Research
Nested polynomial algebras and the exact spectrum of a three-dimensional two-spin oscillator
arxiv.org
October 14, 2026 at 11:25 PM
Using polynomial algebra and deformed-oscillator methods, researchers derived the exact spectrum and complete representations for a three-dimensional oscillator with two coupled spin-1/2 particles.
#QuantumAlgebra #Superintegrability #Research
#QuantumAlgebra #Superintegrability #Research
Superintegrability of a resonant ghostly tri-Hamiltonian model: polynomial first integrals and transcendental completion
https://arxiv.org/pdf/2610.01901
Andreas Fring, Ian Marquette.
https://arxiv.org/pdf/2610.01901
Andreas Fring, Ian Marquette.
https://arxiv.org/abs/2610.01901
arXiv abstract link
arxiv.org
October 6, 2026 at 12:36 PM
Superintegrability of a resonant ghostly tri-Hamiltonian model: polynomial first integrals and transcendental completion
https://arxiv.org/pdf/2610.01901
Andreas Fring, Ian Marquette.
https://arxiv.org/pdf/2610.01901
Andreas Fring, Ian Marquette.
The quasiperiodic superintegrability
October 4, 2026 at 7:00 PM
The quasiperiodic superintegrability
Researchers Find New Invariants for Complex Hamiltonian Systems
Read more:
https://quantumzeitgeist.com/hamiltonian-systems-invariants-three-dimensional-resonance-flow/
Read more:
https://quantumzeitgeist.com/hamiltonian-systems-invariants-three-dimensional-resonance-flow/
Researchers Find New Invariants For Complex Hamiltonian Systems
Can symmetry genuinely extend beyond what’s strictly necessary for describing physical systems? Until now, resonant Hamiltonian models possessed only minimal superintegrability within standard mathematical frameworks. This work demonstrates maximal superintegrability, a functional rank raised from four to five, by admitting carefully constructed transcendental invariants applicable across an open set (Δ>0).
quantumzeitgeist.com
October 5, 2026 at 3:41 AM
Researchers Find New Invariants for Complex Hamiltonian Systems
Read more:
https://quantumzeitgeist.com/hamiltonian-systems-invariants-three-dimensional-resonance-flow/
Read more:
https://quantumzeitgeist.com/hamiltonian-systems-invariants-three-dimensional-resonance-flow/
Andreas Fring, Ian Marquette: Superintegrability of a resonant ghostly tri-Hamiltonian model: polynomial first integrals and transcendental completion https://arxiv.org/abs/2610.01901 https://arxiv.org/pdf/2610.01901 https://arxiv.org/html/2610.01901
October 2, 2026 at 6:54 AM
Andreas Fring, Ian Marquette: Superintegrability of a resonant ghostly tri-Hamiltonian model: polynomial first integrals and transcendental completion https://arxiv.org/abs/2610.01901 https://arxiv.org/pdf/2610.01901 https://arxiv.org/html/2610.01901
Pavel Drozdov: Superintegrability of discrete-time rational Ruijsenaars-Schneider model and deformed polynomial symmetry algebras https://arxiv.org/abs/2609.30065 https://arxiv.org/pdf/2609.30065 https://arxiv.org/html/2609.30065
September 25, 2026 at 6:55 AM
Pavel Drozdov: Superintegrability of discrete-time rational Ruijsenaars-Schneider model and deformed polynomial symmetry algebras https://arxiv.org/abs/2609.30065 https://arxiv.org/pdf/2609.30065 https://arxiv.org/html/2609.30065
Zhuo Chen, Kai Jiang, Nicolai Reshetikhin, Husileng Xiao: Superintegrability of stratified symplectic spaces https://arxiv.org/abs/2609.01953 https://arxiv.org/pdf/2609.01953 https://arxiv.org/html/2609.01953
September 3, 2026 at 6:54 AM
Zhuo Chen, Kai Jiang, Nicolai Reshetikhin, Husileng Xiao: Superintegrability of stratified symplectic spaces https://arxiv.org/abs/2609.01953 https://arxiv.org/pdf/2609.01953 https://arxiv.org/html/2609.01953
Superintegrability of stratified symplectic spaces
https://arxiv.org/pdf/2609.01953
Zhuo Chen, Kai Jiang, Nicolai Reshetikhin, Husileng Xiao.
https://arxiv.org/pdf/2609.01953
Zhuo Chen, Kai Jiang, Nicolai Reshetikhin, Husileng Xiao.
https://arxiv.org/abs/2609.01953
arXiv abstract link
arxiv.org
September 3, 2026 at 4:02 AM
Superintegrability of stratified symplectic spaces
https://arxiv.org/pdf/2609.01953
Zhuo Chen, Kai Jiang, Nicolai Reshetikhin, Husileng Xiao.
https://arxiv.org/pdf/2609.01953
Zhuo Chen, Kai Jiang, Nicolai Reshetikhin, Husileng Xiao.
Averages of Exponentials from the point of view of Superintegrability
https://arxiv.org/pdf/2601.20213
A.Morozov.
https://arxiv.org/pdf/2601.20213
A.Morozov.
https://arxiv.org/abs/2601.20213
arXiv abstract link
arxiv.org
January 29, 2026 at 4:35 AM
Averages of Exponentials from the point of view of Superintegrability
https://arxiv.org/pdf/2601.20213
A.Morozov.
https://arxiv.org/pdf/2601.20213
A.Morozov.
Superintegrability for some $(q,t)$-deformed matrix models
https://arxiv.org/pdf/2510.18524
Fan Liu, Rui Wang, Jie Yang, Wei-Zhong Zhao.
https://arxiv.org/pdf/2510.18524
Fan Liu, Rui Wang, Jie Yang, Wei-Zhong Zhao.
https://arxiv.org/abs/2510.18524
arXiv abstract link
arxiv.org
October 22, 2025 at 4:54 AM
Superintegrability for some $(q,t)$-deformed matrix models
https://arxiv.org/pdf/2510.18524
Fan Liu, Rui Wang, Jie Yang, Wei-Zhong Zhao.
https://arxiv.org/pdf/2510.18524
Fan Liu, Rui Wang, Jie Yang, Wei-Zhong Zhao.
Calogero-Sutherland-type quantum systems, generalized hypergeometric functions and superintegrability for integral chain
https://arxiv.org/pdf/2502.18921
Fan Liu, Rui Wang, Jie Yang, Wei-Zhong Zhao.
https://arxiv.org/pdf/2502.18921
Fan Liu, Rui Wang, Jie Yang, Wei-Zhong Zhao.
https://arxiv.org/abs/2502.18921
arXiv abstract link
arxiv.org
February 27, 2025 at 6:44 AM
Calogero-Sutherland-type quantum systems, generalized hypergeometric functions and superintegrability for integral chain
https://arxiv.org/pdf/2502.18921
Fan Liu, Rui Wang, Jie Yang, Wei-Zhong Zhao.
https://arxiv.org/pdf/2502.18921
Fan Liu, Rui Wang, Jie Yang, Wei-Zhong Zhao.
CMM formula as superintegrability property of unitary model
https://arxiv.org/pdf/2410.03175
A. Mironov, A. Morozov, A. Popolitov
https://arxiv.org/pdf/2410.03175
A. Mironov, A. Morozov, A. Popolitov
CMM formula as superintegrability property of unitary model
arXiv abstract link
arxiv.org
October 8, 2024 at 3:01 AM
CMM formula as superintegrability property of unitary model
https://arxiv.org/pdf/2410.03175
A. Mironov, A. Morozov, A. Popolitov
https://arxiv.org/pdf/2410.03175
A. Mironov, A. Morozov, A. Popolitov
CMM formula as superintegrability property of unitary model
https://arxiv.org/pdf/2410.03175
A. Mironov, A. Morozov, A. Popolitov
https://arxiv.org/pdf/2410.03175
A. Mironov, A. Morozov, A. Popolitov
CMM formula as superintegrability property of unitary model
arXiv abstract link
arxiv.org
October 7, 2024 at 3:00 AM
CMM formula as superintegrability property of unitary model
https://arxiv.org/pdf/2410.03175
A. Mironov, A. Morozov, A. Popolitov
https://arxiv.org/pdf/2410.03175
A. Mironov, A. Morozov, A. Popolitov
Adrian M Escobar-Ruiz, Manuel Fernandez-Guasti
Superintegrability and choreographic obstructions in dihedral $n$-body Hamiltonian systems
https://arxiv.org/abs/2602.17987
Superintegrability and choreographic obstructions in dihedral $n$-body Hamiltonian systems
https://arxiv.org/abs/2602.17987
February 23, 2026 at 7:21 PM
Adrian M Escobar-Ruiz, Manuel Fernandez-Guasti
Superintegrability and choreographic obstructions in dihedral $n$-body Hamiltonian systems
https://arxiv.org/abs/2602.17987
Superintegrability and choreographic obstructions in dihedral $n$-body Hamiltonian systems
https://arxiv.org/abs/2602.17987
Kai Jiang, Guorui Ma, Ian Marquette, Junze Zhang, Yao-Zhong Zhang
Poisson Centralisers and Polynomial Superintegrability for Magnetic Geodesic Flows on Reductive Homogeneous Spaces
https://arxiv.org/abs/2601.01369
Poisson Centralisers and Polynomial Superintegrability for Magnetic Geodesic Flows on Reductive Homogeneous Spaces
https://arxiv.org/abs/2601.01369
January 6, 2026 at 8:42 PM
Kai Jiang, Guorui Ma, Ian Marquette, Junze Zhang, Yao-Zhong Zhang
Poisson Centralisers and Polynomial Superintegrability for Magnetic Geodesic Flows on Reductive Homogeneous Spaces
https://arxiv.org/abs/2601.01369
Poisson Centralisers and Polynomial Superintegrability for Magnetic Geodesic Flows on Reductive Homogeneous Spaces
https://arxiv.org/abs/2601.01369
Luca Cassia, Victor Mishnyakov
Superintegrability of $q,t$-matrix models and quantum toroidal algebra recursions
https://arxiv.org/abs/2510.17360
Superintegrability of $q,t$-matrix models and quantum toroidal algebra recursions
https://arxiv.org/abs/2510.17360
October 21, 2025 at 5:53 AM
Luca Cassia, Victor Mishnyakov
Superintegrability of $q,t$-matrix models and quantum toroidal algebra recursions
https://arxiv.org/abs/2510.17360
Superintegrability of $q,t$-matrix models and quantum toroidal algebra recursions
https://arxiv.org/abs/2510.17360
Sung-Soo Byun, Peter J. Forrester
On the superintegrability of the Gaussian $\beta$ ensemble and its $(q,t)$ generalisation
https://arxiv.org/abs/2505.12927
On the superintegrability of the Gaussian $\beta$ ensemble and its $(q,t)$ generalisation
https://arxiv.org/abs/2505.12927
May 20, 2025 at 4:22 AM
Sung-Soo Byun, Peter J. Forrester
On the superintegrability of the Gaussian $\beta$ ensemble and its $(q,t)$ generalisation
https://arxiv.org/abs/2505.12927
On the superintegrability of the Gaussian $\beta$ ensemble and its $(q,t)$ generalisation
https://arxiv.org/abs/2505.12927
Adrian M Escobar-Ruiz, Manuel Fernandez-Guasti
On the four-body lima\c{c}on choreography: maximal superintegrability and choreographic fragmentation
https://arxiv.org/abs/2504.16403
On the four-body lima\c{c}on choreography: maximal superintegrability and choreographic fragmentation
https://arxiv.org/abs/2504.16403
April 24, 2025 at 4:51 AM
Adrian M Escobar-Ruiz, Manuel Fernandez-Guasti
On the four-body lima\c{c}on choreography: maximal superintegrability and choreographic fragmentation
https://arxiv.org/abs/2504.16403
On the four-body lima\c{c}on choreography: maximal superintegrability and choreographic fragmentation
https://arxiv.org/abs/2504.16403
Victor Mishnyakov
Superintegrability of the Wilson family of matrix models and moments of multivariable orthogonal polynomials
https://arxiv.org/abs/2412.19574
Superintegrability of the Wilson family of matrix models and moments of multivariable orthogonal polynomials
https://arxiv.org/abs/2412.19574
December 30, 2024 at 5:23 AM
Victor Mishnyakov
Superintegrability of the Wilson family of matrix models and moments of multivariable orthogonal polynomials
https://arxiv.org/abs/2412.19574
Superintegrability of the Wilson family of matrix models and moments of multivariable orthogonal polynomials
https://arxiv.org/abs/2412.19574
Claudia Maria Chanu, Giovanni Rastelli
Superintegrability and geometry: a review of the extended Hamiltonian approach
https://arxiv.org/abs/2411.19815
Superintegrability and geometry: a review of the extended Hamiltonian approach
https://arxiv.org/abs/2411.19815
December 2, 2024 at 5:31 AM
Claudia Maria Chanu, Giovanni Rastelli
Superintegrability and geometry: a review of the extended Hamiltonian approach
https://arxiv.org/abs/2411.19815
Superintegrability and geometry: a review of the extended Hamiltonian approach
https://arxiv.org/abs/2411.19815
November 13, 2024 at 5:01 AM
O. Ogulcan Tuncer, I. Yurdusen
Superintegrability in the interaction of two particles with spin
https://arxiv.org/abs/2410.22321
Superintegrability in the interaction of two particles with spin
https://arxiv.org/abs/2410.22321
October 30, 2024 at 4:02 AM
O. Ogulcan Tuncer, I. Yurdusen
Superintegrability in the interaction of two particles with spin
https://arxiv.org/abs/2410.22321
Superintegrability in the interaction of two particles with spin
https://arxiv.org/abs/2410.22321
L. Feher
On the maximal superintegrability of strongly isochronous Hamiltonians
https://arxiv.org/abs/2409.19349
On the maximal superintegrability of strongly isochronous Hamiltonians
https://arxiv.org/abs/2409.19349
October 1, 2024 at 9:01 PM
L. Feher
On the maximal superintegrability of strongly isochronous Hamiltonians
https://arxiv.org/abs/2409.19349
On the maximal superintegrability of strongly isochronous Hamiltonians
https://arxiv.org/abs/2409.19349