Trigonometric version of quantum-classical duality in integrable systems

DOI10.1016/j.nuclphysb.2015.12.005zbMath1332.82064arXiv1510.07509OpenAlexW1837640703MaRDI QIDQ254963

F. Blanchet-Sadri, M. Dambrine

Publication date: 8 March 2016

Published in: Nuclear Physics. B (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1510.07509

Mathematics Subject Classification ID

Dynamic lattice systems (kinetic Ising, etc.) and systems on graphs in time-dependent statistical mechanics (82C20) Many-body theory; quantum Hall effect (81V70) Groups and algebras in quantum theory and relations with integrable systems (81R12) Completely integrable systems and methods of integration for problems in Hamiltonian and Lagrangian mechanics (70H06) Differential geometric methods (tensors, connections, symplectic, Poisson, contact, Riemannian, nonholonomic, etc.) for problems in mechanics (70G45)

Related Items (16)

Quantum \(K\)-theory of quiver varieties and many-body systems ⋮ QKZ-Ruijsenaars correspondence revisited ⋮ 3D mirror symmetry for instanton moduli spaces ⋮ Generalized devil's staircase and RG flows ⋮ Asymmetric six-vertex model and the classical Ruijsenaars-Schneider system of particles ⋮ \((\text{SL}(N), q)\)-opers, the \(q\)-Langlands correspondence, and quantum/classical duality ⋮ Supersymmetric extension of qKZ-Ruijsenaars correspondence ⋮ Quantum-classical duality for Gaudin magnets with boundary ⋮ Self-duality and scattering map for the hyperbolic van Diejen systems with two coupling parameters (with an Appendix by S. Ruijsenaars) ⋮ Lax representation of the hyperbolic van Diejen dynamics with two coupling parameters ⋮ On R-matrix valued Lax pairs for Calogero–Moser models ⋮ On factorized Lax pairs for classical many-body integrable systems ⋮ \(R\)-matrix-valued Lax pairs and long-range spin chains ⋮ Dualities in quantum integrable many-body systems and integrable probabilities. I. ⋮ Quantum-classical correspondence for gl(1|1) supersymmetric Gaudin magnet with boundary ⋮ KZ-Calogero correspondence revisited

Cites Work

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• A q-difference analogue of \(U({\mathfrak g})\) and the Yang-Baxter equation
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• Complete integrability of relativistic Calogero-Moser systems and elliptic function identities
• On trigonometric intertwining vectors and non-dynamical \(R\)-matrix for the Ruijsenaars model
• Quantum integrable models and discrete classical Hirota equations
• Quantum cohomology of flag manifolds and Toda lattices
• The nested Bethe ansatz for ‘all’ closed spin chains

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