Exact solution of the two-axis countertwisting Hamiltonian for the half-integer $J$ case
| Autor: | Pan, Feng, Zhang, Yao-Zhong, Draayer, Jerry P. |
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| Rok vydání: | 2016 |
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| Zdroj: | J. Stat. Mech. (2017) 023104, 17 pages |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1088/1742-5468/aa5a28 |
| Popis: | Bethe ansatz solutions of the two-axis countertwisting Hamiltonian for any (integer and half-integer) $J$ are derived based on the Jordan-Schwinger (differential) boson realization of the $SU(2)$ algebra after desired Euler rotations, where $J$ is the total angular momentum quantum number of the system. It is shown that solutions to the Bethe ansatz equations can be obtained as zeros of the extended Heine-Stieltjes polynomials. Two sets of solutions, with solution number being $J+1$ and $J$ respectively when $J$ is an integer and $J+1/2$ each when $J$ is a half-integer, are obtained. Properties of the zeros of the related extended Heine-Stieltjes polynomials for half-integer $J$ cases are discussed. It is clearly shown that double degenerate level energies for half-integer $J$ are symmetric with respect to the $E=0$ axis. It is also shown that the excitation energies of the `yrast' and other `yrare' bands can all be asymptotically given by quadratic functions of $J$, especially when $J$ is large. Comment: LaTex 12 pages, 3 figures. Major cosmetic type revision. arXiv admin note: text overlap with arXiv:1609.05581 |
| Databáze: | arXiv |
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