Poisson structure and Integrability of a Hamiltonian flow for the inhomogeneous six-vertex model
| Autor: | Rigas, Pete |
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| Rok vydání: | 2023 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | We compute the action-angle variables for a Hamiltonian flow of the inhomogeneous six-vertex model, from a formulation introduced in a 2022 work due to Keating, Reshetikhin, and Sridhar, hence confirming a conjecture of the authors as to whether the Hamiltonian flow is integrable. To demonstrate that such an integrability property of the Hamiltonian holds from the action-angle variables, we make use of previous methods for studying Hamiltonian systems, implemented by Faddeev and Takhtajan, in which it was shown that integrability of a Hamiltonian system holds for the nonlinear Schrodinger's equation by computing action-angle variables from the Poisson bracket, which is connected to the analysis of entries of the monodromy and transfer matrices. For the inhomogeneous six-vertex model, an approach for computing the action-angle variables is possible through formulating several relations between entries of the quantum monodromy, and transfer, matrices, which can be not only be further examined from the structure of $L$ operators, but also from computing several Poisson brackets parameterized from entries of the monodromy matrix. Comment: 105 pages, V2: expanded introduction on Page 1; added further comments on computations with Poisson bracket for integrability of Hamiltonian flow on Page 6; reformatted computations throughout entire paper. Video presentation overview available at: https://www.youtube.com/watch?v=tIO0AwbQp6Q |
| Databáze: | arXiv |
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