nLab Gaudin integrable model

Idea/Definition

A Gaudin integrable model is a special case of Hitchin integrable system where the spectral curve is elliptic.

References

• O. Babelon, D. Bernard, M. Talon, Introduction to classical integrable systems, Cambridge Univ. Press 2003.
• Boris Feigin, Edward Frenkel, Valerio Toledano Laredo, Gaudin models with irregular singularities, math.QA/0612798
• L. Aguirre, G. Felder, A. P. Veselov, Gaudin subalgebras and stable rational curves, arxiv/1004.3253
• E. K. Sklyanin, Separation of variables in the Gaudin model, J. Math. Sci. 47, 2 (1989) 2473-2488, doi
• Branislav Jurčo, Classical Yang-Baxter equations and quantum integrable systems (Gaudin models), pp. 1616-6361 in Springer Lect. Notes in Physics 370 (1990) doi
• B. Feigin, E. Frenkel, N. Reshetikhin, Gaudin model, Bethe Ansatz and critical level, Commun. Math. Phys 166 (1994), pp. 27–62, euclid, MR1309540
• L.G. Rybnikov, Uniqueness of higher Gaudin Hamiltonians, doi, Reports on Math. Phys. 61, 2 (2008) 247-252
• B. Enriquez, V. Rubtsov, Hitchin systems, higher Gaudin Hamiltonians and r-matrices, Math. Res. Letters 3 (1996) n° 3, 343-357, alg-geom/9503010
• K. Takesaki, Gaudin model, KZ equation and an isomonodromic problem on the torus, 44, 2 (1998) 143-156, doi, hep-th/9711058
• M. Gaudin, La fonction d’onde de Bethe, Paris: Masson 1983, xvi+331.
• M. Gaudin, Diagonalisation d’une classe d’hamiltoniens de spin, J. Physique 37, 1087–1098 (1976).
• (physics applications:) G. Ortiz, R. Somma, J. Dukelsky, S. Rombouts, Exactly-solvable models derived from a generalized Gaudin algebra, cond-mat/0407429

Quantization of the Gaudin model:

• V. Talalaev, The quantum Gaudin system, Funct. Anal. Appl. 40, 73–77 (2006) ( Квантовая система Годена, Функц. анализ и его прил. 40, вып. 1, 2006, с. 86–91, pdf)