Quantum spin chains and integrable many-body systems of classical mechanics

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5 Citations (Scopus)

Abstract

This note is a review of the recently revealed intriguing connection between integrable quantum spin chains and integrable many-body systems of classical mechanics. The essence of this connection lies in the fact that the spectral problem for quantum Hamiltonians of the former models is closely related to a sort of inverse spectral problem for Lax matrices of the latter ones. For simplicity, we focus on the most transparent and familiar case of spin chains on N sites constructed by means of the GL(2)-invariant R-matrix. They are related to the classical Ruijsenaars- Schneider system of N particles, which is known to be an integrable deformation of the Calogero-Moser system. As an explicit example the case N = 2 is considered in detail.

Original languageEnglish
Title of host publicationNonlinear Mathematical Physics and Natural Hazards - Selected Papers from the International School and Workshop
EditorsMihaela Kouteva-Guentcheva, Boyka Aneva, Mihaela Kouteva-Guentcheva, Boyka Aneva
PublisherSpringer Science and Business Media, LLC
Pages29-48
Number of pages20
ISBN (Electronic)9783319143279, 9783319143279
DOIs
Publication statusPublished - 2015
Externally publishedYes
EventInternational School and Workshop on Nonlinear Mathematical Physics and Natural Hazards, 2013 - Sofia, Bulgaria
Duration: 28 Nov 20132 Dec 2013

Publication series

NameSpringer Proceedings in Physics
Volume163
ISSN (Print)0930-8989
ISSN (Electronic)1867-4941

Conference

ConferenceInternational School and Workshop on Nonlinear Mathematical Physics and Natural Hazards, 2013
Country/TerritoryBulgaria
CitySofia
Period28/11/132/12/13

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