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arXiv:0805.4495 · Regular and Chaotic Dynamics

New formula for the eigenvectors of the Gaudin model in the sl(3) case

Č. Burdík, Ondřej Navrátil

Published Oct 1, 2008• 2 citations
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Abstract

We propose new formulas for eigenvectors of the Gaudin model in the sl(3) case. The central point of the construction is the explicit form of some operator P, which is used for derivation of eigenvalues given by the formula $$ \left| {w_1 ,w_2 )} \right. = \sum\limits_{n = 0}^\infty {\frac{{P^n }} {{n!}}} \left| {w_1 ,w_2 ,0} \right\rangle , $$ where w 1, w 2 fulfil the standard well-know Bethe Ansatz equations.

DOI
10.1134/s156035470805002x

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We propose new formulas for eigenvectors of the Gaudin model in the sl(3) case. The central point of the construction is the explicit form of some operator P, which is used for derivation of eigenvalues given by the formula ∣w1,w2)=∑n=0∞Pnn!∣w1,w2,0⟩,\left| {w_1 ,w_2 )} \right. = \sum\limits_{n = 0}^\infty {\frac{{P^n }} {{n!}}} \left| {w_1 ,w_2 ,0} \right\rangle ,∣w1​,w2​)=n=0∑∞​n!Pn​∣w1​,w2​,0⟩, where w 1, w 2 fulfil the standard well-know Bethe Ansatz equations.
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On a new form of Bethe ansatz equations and separation of variables in the sl3\mathfrak{s}\mathfrak{l}_3 sl3​ Gaudin model
A new form of Bethe ansatz equations is introduced. A version of a separation of variables for the quantum sl3\mathfrak{s}\mathfrak{l}_3 sl3​ Gaudin model is presented.