Quantum Integrals for a Semi-Infinite q-Boson System with Boundary Interactions

Diejen, J. F. van; Emsiz, E.

doi:10.3842/sigma.2015.037

Cited by 3 publications

(3 citation statements)

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“…An interesting question resulting from our discussion is a possible extension of our construction of quantum Bäcklund transformations to the continuum limit, where one obtains the quantum nonlinear Schrödinger model, as well as to different boundary conditions; see e.g. [31,34] for a discussion of the q-boson system with more exotic boundaries. We hope to address these and related questions in future work.…”

Section: Open Questionsmentioning

confidence: 99%

From quantum Bäcklund transforms to topological quantum field theory

Korff¹

2016

J. Phys. A: Math. Theor.

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We derive the quantum analogue of a Bäcklund transformation for the quantised Ablowitz-Ladik chain, a space discretisation of the nonlinear Schrödinger equation. The quantisation of the Ablowitz-Ladik chain leads to the q-boson model. Using a previous construction of Baxter's Q-operator for this model by the author, a set of functional relations is obtained which matches the relations of a one-variable classical Bäcklund transform to all orders in . We construct also a second Q-operator and show that it is closely related to the inverse of the first. The multi-Bäcklund transforms generated from the Q-operator define the fusion matrices of a 2D TQFT and we derive a linear system for the solution to the quantum Bäcklund relations in terms of the TQFT fusion coefficients.

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Section: Open Questionsmentioning

confidence: 99%

From quantum Bäcklund transforms to topological quantum field theory

Korff¹

2016

J. Phys. A: Math. Theor.

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“…. , x n ; q, 0, t l ) that diagonalizes Ruijsenaars's q-difference Toda chain with one-sided integrable boundary interactions of Askey-Wilson type [DE1]. The corresponding branching polynomial for P λ (x 1 , .…”

Section: Branching Polynomials [De3]mentioning

confidence: 99%

“…, x n ; q, 0, t l ) simplifies considerably when one or more of the parameters t 1 , t 2 or t 3 vanish. From the perspective of Ruijsenaars' q-difference Toda chain, such parameter reductions correspond to degenerations of the interaction at the boundary [DE1,Sec. 7].…”

Section: Branching Polynomials [De3]mentioning

confidence: 99%