A non-symmetric Yang-Baxter algebra for the quantum nonlinear Schrödinger model

Vlaar, Bart (2011) A non-symmetric Yang-Baxter algebra for the quantum nonlinear Schrödinger model. PhD thesis, University of Glasgow.

Abstract

We study certain non-symmetric wavefunctions associated to the quantum nonlinear Schrödinger (QNLS) model, introduced by Komori and Hikami using representations of the degenerate
affine Hecke algebra. In particular, they can be generated using a vertex operator formalism analogous to the recursion that defines the symmetric QNLS wavefunction in the quantum inverse scattering method. Furthermore, some of the commutation relations encoded in the Yang-Baxter equation are generalized to the non-symmetric case.

• Item Type: Thesis (PhD)
• Qualification Level: Doctoral
• Keywords: Quantum integrable systems, Quantum nonlinear Schrödinger model, Bethe ansatz, Quantum inverse scattering method, Yang-Baxter equation, Yangians, Vertex operators, Baxter’s Q-operator, Affine Hecke algebras, Weyl groups, Dunkl operators, Representation theory.
• Subjects: Q Science > QC Physics; Q Science > QA Mathematics
• Colleges/Schools: College of Science and Engineering > School of Mathematics and Statistics > Mathematics
• Supervisor's Name: Korff, Dr. Christian
• Date of Award: 2011
• Depositing User: Mr Bart Vlaar
• Unique ID: glathesis:2011-3251
• Copyright: Copyright of this thesis is held by the author.
• Date Deposited: 12 Mar 2012
• Last Modified: 10 Dec 2012 14:05
• URI: https://theses.gla.ac.uk/id/eprint/3251