Spectral analysis of an open $q$-difference Toda chain with two-sided boundary interactions on the finite integer lattice
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| Format: | Preprint |
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2023
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| _version_ | 1866909117253156864 |
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| author | van Diejen, Jan Felipe |
| author_facet | van Diejen, Jan Felipe |
| contents | A quantum $n$-particle model consisting of an open $q$-difference Toda chain with two-sided boundary interactions is placed on a finite integer lattice. The spectrum and eigenbasis are computed by establishing the equivalence with a previously studied $q$-boson model from which the quantum integrability is inherited. Specifically, the $q$-boson-Toda correspondence in question yields Bethe Ansatz eigenfunctions in terms of hyperoctahedral Hall-Littlewood polynomials and provides the pertinent solutions of the Bethe Ansatz equations via the global minima of corresponding Yang-Yang type Morse functions. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2304_05466 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Spectral analysis of an open $q$-difference Toda chain with two-sided boundary interactions on the finite integer lattice van Diejen, Jan Felipe Mathematical Physics Exactly Solvable and Integrable Systems Primary: 33D52, Secondary: 05E05, 81Q35, 81Q80, 81U15, 82B23 A quantum $n$-particle model consisting of an open $q$-difference Toda chain with two-sided boundary interactions is placed on a finite integer lattice. The spectrum and eigenbasis are computed by establishing the equivalence with a previously studied $q$-boson model from which the quantum integrability is inherited. Specifically, the $q$-boson-Toda correspondence in question yields Bethe Ansatz eigenfunctions in terms of hyperoctahedral Hall-Littlewood polynomials and provides the pertinent solutions of the Bethe Ansatz equations via the global minima of corresponding Yang-Yang type Morse functions. |
| title | Spectral analysis of an open $q$-difference Toda chain with two-sided boundary interactions on the finite integer lattice |
| topic | Mathematical Physics Exactly Solvable and Integrable Systems Primary: 33D52, Secondary: 05E05, 81Q35, 81Q80, 81U15, 82B23 |
| url | https://arxiv.org/abs/2304.05466 |