Quantum inverse scattering method: Difference between revisions

Revision as of 12:34, 23 September 2011

Revision as of 15:52, 27 September 2011

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Quantum inverse scattering method starts by quantization of Lax representation and reproduce results of Bethe ansatz.

Actually it permits to rewrite Bethe ansatz in a new form: algebraic Bethe ansatz. This led to further progress in understanding of quantum [[Integrable system]] like [[Heisenberg model (quantum)]],

quantum [[Nonlinear Schrödinger equation ]] (also known as [[Lieb-Liniger Model]] or [[Bose gas]] with delta interaction) and [[Hubbard model]]. Theory of correlation functions was developed: determinant representations, description by differential equations and Riemann-Hilbert problem and asymptotic. Explicit expression for higher [[Conservation law]]. In mathematics it led to formulation of [[quantum groups]]. Especially interesting one is [[Yangian]], the center of the Yangian is given by quantum determinant. Essential progress was achieved in study of [[6 vertexIce-type model]]: the bulk free energy of six vertex model depends on boundary conditions in [[thermodynamic limit]].