Quantum inverse scattering method: Difference between revisions

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The quantum inverse scattering method relates two different approaches:

1) The [[Bethe ansatz ]], a method of solving integrable quantum models in one space and one time dimension;

2) the [[Inverse scattering transform]], a method of solving classical integrable differential equations of the evolutionary type.

An important concept in the [[Inverse scattering transform]] is the [[Lax representation]]; the quantum inverse scattering method starts by the quantization of Lax representation and reproduces the results of the Bethe ansatz.

In fact it allows the Bethe ansatz to be written in a new form: the algebraic Bethe ansatz. This led to further progress in the understanding of quantum [[Integrable systems]] for example: a) the [[Heisenberg model (quantum)]],

b) the quantum [[Nonlinear Schrödinger equation ]] (also known as the [[Lieb-Liniger Model]] or the [[Tonks–Girardeau gas]]) and c) the [[Hubbard model]]. The

theory of correlation functions was developed: determinant representations, descriptions by differential equations and the [[Riemann-Hilbert problem]].

Asymptotics of correlation functions (even for space, time and temperature dependence) were evaluated in 1991. Explicit expressions for the higher [[conservation laws]]