☆ 4.4 Article

Anisotropic Spin Generalization of Elliptic Macdonald-Ruijsenaars Operators and R-Matrix Identities

ANNALES HENRI POINCARE (2023)

Related references

Note: Only part of the references are listed.

Article Mathematics, Applied

Elliptic generalisation of integrable q-deformed anisotropic Haldane-Shastry long-range spin chain

M. Matushko et al.

Summary: We describe an integrable elliptic q-deformed anisotropic long-range spin chain. The Polychronakos freezing trick is applied to derive a set of commuting Hamiltonians for this spin chain, which is constructed using the elliptic Baxter-Belavin GL(M)R-matrix. The freezing trick is reduced to a set of elliptic function identities, serving as equilibrium conditions in the classical spinless Ruijsenaars-Schneider model.

NONLINEARITY (2023)

Add to Collection

Article Mathematics

Elliptic Ruijsenaars Difference Operators on Bounded Partitions

Jan van Diejen et al.

Summary: By applying a truncation condition to the parameters, the elliptic Ruijsenaars difference operators are confined to a finite lattice of points determined by bounded partitions. Using polynomials on the joint spectrum, a corresponding orthogonal basis of joint eigenfunctions is constructed. In the trigonometric limit, this leads to the diagonalization of the truncated Macdonald difference operators using a finite basis of Macdonald polynomials.

INTERNATIONAL MATHEMATICS RESEARCH NOTICES (2022)

Add to Collection

Article Physics, Particles & Fields

Field analogue of the Ruijsenaars-Schneider model

A. Zabrodin et al.

Summary: This article proposes a field extension of the classical elliptic Ruijsenaars-Schneider model and defines and derives it through two different methods. The first method defines the model through the trace of the L-matrix, resulting in a lattice field analogue. The second method defines the model through the investigation of elliptic families of solutions to the 2D Toda equation and proves that their equations of motion are Hamiltonian. The models obtained from these two methods are equivalent.

JOURNAL OF HIGH ENERGY PHYSICS (2022)

Add to Collection

Article Physics, Multidisciplinary

QUADRATIC ALGEBRAS BASED ON SL(NM) ELLIPTIC QUANTUM R-MATRICES

I. A. Sechin et al.

Summary: In this study, a quadratic quantum algebra is constructed based on the dynamical RLL-relation for the quantum R-matrix associated with SL(NM)-bundles with a nontrivial characteristic class over an elliptic curve. This R-matrix generalizes existing matrices and the obtained quadratic relations provide a new set of relationships.

THEORETICAL AND MATHEMATICAL PHYSICS (2021)

Add to Collection

Article Physics, Particles & Fields

Duality in elliptic Ruijsenaars system and elliptic symmetric functions

A. Mironov et al.

Summary: This study demonstrates that the symmetric elliptic polynomials are eigenfunctions of the elliptic Ruijsenaars-Schneider Hamiltonians, while their orthogonal complements are eigenfunctions of the elliptic reduction of the Koroteev-Shakirov Hamiltonians. These two sets of eigenfunctions are related by a mysterious orthogonality transformation and the coordinates xi only appear after the Miwa transform, which explains the difficulties in obtaining self-dual Hamiltonians from the double elliptic version of the KS Hamiltonians.

EUROPEAN PHYSICAL JOURNAL C (2021)

Add to Collection

Article Physics, Mathematical

On the Hamiltonian formulation of the trigonometric spin Ruijsenaars-Schneider system

Oleg Chalykh et al.

LETTERS IN MATHEMATICAL PHYSICS (2020)

Add to Collection

Article Mathematics, Applied

Hyperbolic Spin Ruijsenaars-Schneider Model from Poisson Reduction

Gleb E. Arutyunov et al.

PROCEEDINGS OF THE STEKLOV INSTITUTE OF MATHEMATICS (2020)

Add to Collection

Article Physics, Mathematical

Quantum Lax Pairs via Dunkl and Cherednik Operators

Oleg Chalykh

COMMUNICATIONS IN MATHEMATICAL PHYSICS (2019)

Add to Collection

Article Physics, Multidisciplinary

Trigonometric Integrable Tops from Solutions of Associative Yang-Baxter Equation

T. Krasnov et al.

ANNALES HENRI POINCARE (2019)

Add to Collection

Article Physics, Particles & Fields

Quantum trace formulae for the integrals of the hyperbolic Ruijsenaars-Schneider model

Gleb Arutyunov et al.

JOURNAL OF HIGH ENERGY PHYSICS (2019)

Add to Collection

Article Physics, Multidisciplinary

RELATIVISTIC INTERACTING INTEGRABLE ELLIPTIC TOPS

A. V. Zotov

THEORETICAL AND MATHEMATICAL PHYSICS (2019)

Add to Collection

Article Physics, Particles & Fields

Generalized model of interacting integrable tops

A. Grekov et al.

JOURNAL OF HIGH ENERGY PHYSICS (2019)

Add to Collection

Article Physics, Particles & Fields

Poisson-Lie analogues of spin Sutherland models

L. Feher

NUCLEAR PHYSICS B (2019)

Add to Collection

Article Physics, Multidisciplinary

On R-matrix valued Lax pairs for Calogero-Moser models

A. Grekov et al.

JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL (2018)

Add to Collection

Article Astronomy & Astrophysics

R-matrix-valued Lax pairs and long-range spin chains

I. Sechin et al.

PHYSICS LETTERS B (2018)

Add to Collection

Article Physics, Multidisciplinary

Calogero-Moser Model and R-Matrix Identities

A. V. Zotov

THEORETICAL AND MATHEMATICAL PHYSICS (2018)

Add to Collection

Article Materials Science, Multidisciplinary

Resurrecting the partially isotropic Haldane-Shastry model

Jules Lamers

PHYSICAL REVIEW B (2018)

Add to Collection

Article Physics, Multidisciplinary

QUANTUM BAXTER-BELAVIN R-MATRICES AND MULTIDIMENSIONAL LAX PAIRS FOR PAINLEVE VI

A. M. Levin et al.

THEORETICAL AND MATHEMATICAL PHYSICS (2015)

Add to Collection

Article Physics, Particles & Fields

Relativistic classical integrable tops and quantum R-matrices

A. Levin et al.

JOURNAL OF HIGH ENERGY PHYSICS (2014)

Add to Collection

Article Physics, Multidisciplinary

Characteristic classes of SL(N, C)-bundles and quantum dynamical elliptic R-matrices

A. Levin et al.

JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL (2013)

Add to Collection

Article Mathematics

Classical Yang-Baxter equation and the A∞-constraint

A Polishchuk

ADVANCES IN MATHEMATICS (2002)

Add to Collection

© Peeref 2019-2024. All rights reserved.