Quantum inverse scattering method: Difference between revisions

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{{expert needed|1=Physics|reason=copyedit, create lede|date=May 2019}}

In [[quantum physics]], the '''quantum inverse scattering method''' or the '''algebraic Bethe ansatz''' is a method for solving [[integrable system|integrable model]]s in 1+1 dimensions, introduced by [[Ludvig Faddeev|L. D. Faddeev]] in 1979.

The quantum inverse scattering method relates two different approaches:

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#the [[inverse scattering transform]], a method of solving classical integrable differential equations of the evolutionary type.

This method led to the formulation of [[quantum group]]s. Especially, interestingin isparticular the [[Yangian]],. and theThe center of the Yangian is, given by the [[quantum determinant]] plays a prominent role in the method.

An important concept in the [[inverse scattering transform]] is the [[Lax pair|Lax representation]];. theThe quantum inverse scattering method starts by the [[quantization (physics)|quantization]] of the 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''.<ref>See for example lectures by N.A. Slavnov {{arXiv|1804.07350}}</ref> This led to further progress in the understanding of quantum [[integrable system]]s, such as the [[quantum Heisenberg model]], the quantum [[Nonlinear Schrödinger equation]] (also known as the [[Lieb–Liniger model]] or the [[Tonks–Girardeau gas]]) and the [[Hubbard model]].

The theory of [[correlation function]]s was developed {{when|date=November 2015}}, relating determinant representations, descriptions by differential equations and the [[Riemann–Hilbert problem]]. Asymptotics of correlation functions which include space, time and temperature dependence were evaluated in 1991.