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Title: Quantum integrable systems, non-skew-symmetric r-matrices and algebraic Bethe ansatz

Abstract

We prove the integrability of the general quantum Hamiltonian systems governed by an arbitrary non-skew-symmetric, so(3)-valued, nondynamical classical r-matrix with spectral parameters. We consider the most interesting example of these quantum integrable systems, namely, the so(3) 'generalized Gaudin systems' in detail. In the case of an arbitrary r-matrix which is 'diagonal' in the sl(2) basis we calculate the spectrum and the eigenvalues of the corresponding Hamiltonians using the algebraic Bethe ansatz technique.

Authors:
 [1]
  1. Bogoliubov Institute for Theoretical Physics, Institute of Mathematics of NASU, Metrologichna Strasse, 14-b, Kiev 03143 (Ukraine)
Publication Date:
OSTI Identifier:
20929643
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Mathematical Physics; Journal Volume: 48; Journal Issue: 2; Other Information: DOI: 10.1063/1.2435085; (c) 2007 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ALGEBRA; EIGENFUNCTIONS; EIGENVALUES; HAMILTONIANS; INTEGRAL CALCULUS; LATTICE FIELD THEORY; R MATRIX; SO-3 GROUPS

Citation Formats

Skrypnyk, T. Quantum integrable systems, non-skew-symmetric r-matrices and algebraic Bethe ansatz. United States: N. p., 2007. Web. doi:10.1063/1.2435085.
Skrypnyk, T. Quantum integrable systems, non-skew-symmetric r-matrices and algebraic Bethe ansatz. United States. doi:10.1063/1.2435085.
Skrypnyk, T. Thu . "Quantum integrable systems, non-skew-symmetric r-matrices and algebraic Bethe ansatz". United States. doi:10.1063/1.2435085.
@article{osti_20929643,
title = {Quantum integrable systems, non-skew-symmetric r-matrices and algebraic Bethe ansatz},
author = {Skrypnyk, T.},
abstractNote = {We prove the integrability of the general quantum Hamiltonian systems governed by an arbitrary non-skew-symmetric, so(3)-valued, nondynamical classical r-matrix with spectral parameters. We consider the most interesting example of these quantum integrable systems, namely, the so(3) 'generalized Gaudin systems' in detail. In the case of an arbitrary r-matrix which is 'diagonal' in the sl(2) basis we calculate the spectrum and the eigenvalues of the corresponding Hamiltonians using the algebraic Bethe ansatz technique.},
doi = {10.1063/1.2435085},
journal = {Journal of Mathematical Physics},
number = 2,
volume = 48,
place = {United States},
year = {Thu Feb 15 00:00:00 EST 2007},
month = {Thu Feb 15 00:00:00 EST 2007}
}