Quantum inverse scattering method: Difference between revisions

Revision as of 12:10, 23 September 2011

Revision as of 12:34, 23 September 2011

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2) [[Bethe ansatz ]] is a method of solving quantum models in one space and one time dimension.

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[[Conservation lawslaw]]. In mathematics it led to formulation of [[quantum groups]]. Especially interesting one is [[Yangian]]. Essential progress was achieved in study of [[6 vertex model]]: the bulk free energy depends on boundary conditions in [[thermodynamic limit]].