71 citations · 117 across the 5 of their papers we have counts for
5 papers
Eigenproblem for Jacobi matrices: hypergeometric series solution
Vadim B. Kuznetsov, Evgeny K. Sklyanin
We study the perturbative power-series expansions of the eigenvalues and eigenvectors of a general tridiagonal (Jacobi) matrix of dimension d. The(small) expansion parameters are b…
Separation of Variables in the Elliptic Gaudin Model
Evgueni K. Sklyanin, Takashi Takebe
For the elliptic Gaudin model (a degenerate case of XYZ integrable spin chain) a separation of variables is constructed in the classical case. The corresponding separated coordinat…
Separation of variables and integral relations for special functions
Vadim B. Kuznetsov, Evgueni K. Sklyanin
We show that the method of separation of variables gives a natural generalisation of integral relations for classical special functions of one variable. The approach is illustrated…
Algebraic Bethe Ansatz for XYZ Gaudin model
E. K. Sklyanin, T. Takebe
The eigenvectors of the Hamiltionians of the XYZ Gaudin model are constructed by means of the algebraic Bethe Ansatz. The construction is based on the quasi-classical limit of the…
Separation of variables in the type Jack polynomials
V. B. Kuznetsov, E. K. Sklyanin
An integral operator is constructed performing a separation of variables for the 3-particle quantum Calogero-Sutherland (CS) model. Under the action of the CS eigenfunction…