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# Generating function for the Gaudin model with boundar

Seminário do GFM
IIIUL, Sala B3-01
2013-12-03 15:30 .. 16:30
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Nenad Manojlović (GFMUL/Univ. Algarve)

Following Sklyanin’s proposal in the periodic case, we derive the generating function for the Gaudin model with boundary. Our derivation is based on the quasi-classical expansion of the linear combination of the transfer matrix of the XXX chain and the central element, the so-called Sklyanin determinant. The corresponding Gaudin Hamiltonians with boundary terms are obtained as the residues of the generating function. We study the relevant algebraic structure for the algebraic Bethe ansatz. In the case when the two boundary matrices are both upper-triangular, we implement the algebraic Bethe ansatz, obtaining the eigenvalues of the generating function and the corresponding Bethe states.