Aspects of the inverse problem for the Toda chain

DOI10.1063/1.4848778zbMath1294.81384arXiv1307.4052OpenAlexW3104959889MaRDI QIDQ5412784

Karol Kajetan Kozlowski

Publication date: 28 April 2014

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1307.4052

zbMATH Keywords

HamiltonianintegrabilityLax methodmonodromy matrixToda chain

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Inverse scattering problems in quantum theory (81U40) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Many-body theory; quantum Hall effect (81V70) Monodromy on manifolds (58K10) Special quantum systems, such as solvable systems (81Q80)

Related Items (5)

Difference equation for the Heckman-Opdam hypergeometric function and its confluent Whittaker limit ⋮ On the separation of variables for the modular XXZ magnet and the lattice sinh-Gordon models ⋮ Integrable boundary interactions for Ruijsenaars' difference Toda chain ⋮ Wave functions for quantum integrable particle systems via partial confluences of multivariate hypergeometric functions ⋮ On the form factors of local operators in the Bazhanov-Stroganov and chiral Potts models

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Action-angle map and duality for the open Toda lattice in the perspective of Hamiltonian reduction
• Wave functions of the Toda chain with boundary interaction
• Complete set of eigenfunctions of the quantum Toda chain
• The solution to a generalized Toda lattice and representation theory
• Quantum completely integrable systems connected with semi-simple Lie algebras
• Equations in dual variables for Whittaker functions
• Classical and quantum mechanical systems of Toda-lattice type. III: Joint eigenfunctions of the quantized systems
• Action-angle maps and scattering theory for some finite-dimensional integrable systems. III: Sutherland type systems and their duals
• Unitarity of the SoV transform for the Toda chain
• Transition function for the Toda chain
• Partition function of the eight-vertex lattice model
• Integral representations for the eigenfunctions of quantum open and periodic Toda chains from the QISM formalism
• Bispectrality for the quantum open Toda chain
• TBA for the Toda chain
• Quantization of Integrable Systems and Four Dimensional Gauge Theories
• On the form factors of local operators in the lattice sine–Gordon model
• Non-diagonal open spin-1/2XXZquantum chains by separation of variables: complete spectrum and matrix elements of some quasi-local operators
• The periodic Toda chain and a matrix generalization of the Bessel function recursion relations
• A complete solution of the periodic Toda problem
• Stationary Phase Integrals, Quantum Toda Lattices, Flag Manifolds and the Mirror Conjecture
• Large distance asymptotic behaviour of the emptiness formation probability of theXXZspin-1/2 Heisenberg chain
• On the quantum inverse problem for the closed Toda chain
• Quantum projectors and local operators in lattice integrable models
• The Toda lattice. II. Existence of integrals
• On the quantum inverse scattering problem.
• Noncompact Heisenberg spin magnets from high-energy QCD. I: Baxter Q-operator and separation of variables

This page was built for publication: Aspects of the inverse problem for the Toda chain