Lie algebra deformations and the exact solutions of integrable quantum many-body systems

Lee, Yuan-Harng (2012). Lie algebra deformations and the exact solutions of integrable quantum many-body systems PhD Thesis, School of Mathematics & Physics, The University of Queensland.

       
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Author Lee, Yuan-Harng
Thesis Title Lie algebra deformations and the exact solutions of integrable quantum many-body systems
School, Centre or Institute School of Mathematics & Physics
Institution The University of Queensland
Publication date 2012
Thesis type PhD Thesis
Supervisor Yao-Zhong Zhang
Jon Links
Total pages 117
Total black and white pages 117
Language eng
Subjects 010501 Algebraic Structures in Mathematical Physics
010502 Integrable Systems (Classical and Quantum)
0105 Mathematical Physics
Formatted abstract
In this body of work, we will examine two classes of Lie algebra deformations and their appli- cation to the exact solutions of various quantum integrable systems.

The first class of Lie algebra deformations are polynomial deformations of the A1 Lie algebra. We construct unitary representations of these algebras in terms of bosonic and spin operators as well as obtain their single-variable differential operator realizations. Using these results, we obtain the exact Bethe ansatz solutions of a variety of quantum integrable systems such as the Bose-Hubbard and Tavis-Cummings model.

The second class of Lie algebra deformations are the so-called quasi-Gaudin algebra. This algebra was introduced to construct integrable systems which are only quasi-exactly solvable. Using a suitable representation this algebra, we obtain partial solutions for a class of bosonic models which do not preserve U(1) symmetry
Keyword Integrable quantum systems
Quasi-exactly solvable systems
Polynomial algebras
BEC systems
Spin-boson systems
Gaudin models

 
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Created: Wed, 10 Oct 2012, 16:08:29 EST by Yuan Lee on behalf of Scholarly Communication and Digitisation Service