Aspects of the inverse problem for the Toda chain

Abstract

We generalize Babelon's approach to equations in dual variables so as to be able to treat new types of operators which we build out of the sub-constituents of the model's monodromy matrix. Further, we also apply Sklyanin's recent monodromy matrix identities so as to obtain equations in dual variables for yet other operators. The schemes discussed in this paper appear to be universal and thus, in principle, applicable to many models solvable through the quantum separation of variables.

29 pages, V2 minor corrections

References in corpus (3)

• Non-diagonal open spin-1/2 XXZ quantum chains by separation of variables: Complete spectrum and matrix elements of some quasi-local operators
• Bispectrality for the quantum open Toda chain
• Action-angle map and duality for the open Toda lattice in the perspective of Hamiltonian reduction

Cited by in corpus (6)

• Difference equation for the Heckman-Opdam hypergeometric function and its confluent Whittaker limit
• Integrable boundary interactions for Ruijsenaars' difference Toda chain
• On the separation of variables for the modular XXZ magnet and the lattice Sinh-Gordon models
• Bispectral dual difference equations for the quantum Toda chain with boundary perturbations
• Wave functions for quantum integrable particle systems via partial confluences of multivariate hypergeometric functions
• On the equilibrium measure for the Lukyanov integral