Quantum inverse scattering method: Difference between revisions

Revision as of 16:05, 27 September 2011

Revision as of 13:00, 25 October 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]] for example a) [[Heisenberg model (quantum)]],

b) quantum [[Nonlinear Schrödinger equation ]] (also known as [[Lieb-Liniger Model]] or [[Tonks–Girardeau gas]]) and c) [[Hubbard model]]... Theory of correlation functions was developed: determinant representations, description by differential equations and [[Riemann-Hilbert problem]]. Asymptotic of correlation functions (even for space, time and temperature dependent) was evaluated in 1991. Explicit expression for higher [[Conservationconservation lawlaws]] was obtained in 1989. In mathematics quantum inverse scattering method led to formulation of [[quantum groups]]. Especially interesting is [[Yangian]], the center of the Yangian is given by quantum determinant. Essential progress was achieved in study of [[Ice-type model]]: the bulk free energy of six vertex model depends on boundary conditions even in [[thermodynamic limit]].