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Quantum inverse scattering method

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This is an old revision of this page, as edited by Korepin (talk | contribs) at 12:51, 27 February 2010. The present address (URL) is a permanent link to this revision, which may differ significantly from the current revision.

Quantum inverse scattering method relates two different approaches: 1)Inverse scattering transform is a method of solving classical integrable differential equations of evolutionary type. Important concept is Lax representation . 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 lead to further progress in understanding of Heisenberg model (quantum) , quantum Nonlinear Schrödinger equation and Hubbard model.


In mathematics, the quantum inverse scattering method is a method for solving integrable models in 1+1 dimensions introduced by L. D. Faddeev in about 1979.

References

  • Faddeev, L. (1995), "Instructive history of the quantum inverse scattering method", Acta Applicandae Mathematicae., 39 (1): 69–84, ISSN 0167-8019, MR1329554
  • Korepin, V. E.; Bogoliubov, N. M.; Izergin, A. G. (1993), Quantum inverse scattering method and correlation functions, Cambridge Monographs on Mathematical Physics, Cambridge University Press, ISBN 978-0-521-37320-3, MR1245942
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