Combinatorical and Algebraic Structures Seminar
Session details
| Date: | 14.10.2008 |
| Speaker: | Čestmír Burdík, FJFI, České vysoké učení technické |
| Title: | New Formula for the Eigenvectors of the Gaudin Model in the $\mathrm{sl}(3)$ Case |
| Abstract: | (spoluautoři: O. Navrátil) We propose new formulas for eigenvectors of the Gaudin model in the $\mathrm{sl}(3)$ case. The central point of the construction is the explicit form of some operator $\boldsymbol{\mathrm{P}}$, which is used for derivation of eigenvalues given by the formula \[|\boldsymbol{w}_1, \boldsymbol{w}_2 ) =\sum_{n=0}^{\infty} \frac{\boldsymbol{\mathrm{P}}^n}{n!} |\boldsymbol{w}_1,\boldsymbol{w}_2,0\rangle\,,\] where $\boldsymbol{w}_1$, $\boldsymbol{w}_2$ fulfil the standard well-know Bethe Ansatz equations. |
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