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Explicit Solution of the (Quantum) Elliptic Calogero-Sutherland Model
KTH, School of Engineering Sciences (SCI), Theoretical Physics, Mathematical Physics.
2014 (English)In: Annales de l'Institute Henri Poincare. Physique theorique, ISSN 1424-0637, E-ISSN 1424-0661, Vol. 15, no 4, 755-791 p.Article in journal (Refereed) Published
Abstract [en]

The elliptic Calogero-Sutherland model is a quantum many body system of identical particles moving on a circle and interacting via two body potentials proportional to the Weierstrass -function. It also provides a natural many-variable generalization of the Lam, equation. Explicit formulas for the eigenfunctions and eigenvalues of this model as infinite series are obtained, to all orders and for arbitrary particle numbers and coupling parameters. These eigenfunctions are an elliptic deformation of the Jack polynomials. The absolute convergence of these series is proved in special cases, including the two-particle (=Lam,) case for non-integer coupling parameters and sufficiently small elliptic deformation.

Place, publisher, year, edition, pages
2014. Vol. 15, no 4, 755-791 p.
Keyword [en]
Many-Body Systems, Jack Polynomials, Lame Functions, Lie-Algebras, Bethe-Ansatz, Eigenvectors, Identities, Formulas, Exchange, Operator
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URN: urn:nbn:se:kth:diva-144347DOI: 10.1007/s00023-013-0254-8ISI: 000333111400006ScopusID: 2-s2.0-84896400376OAI: diva2:713467
Swedish Research Council

QC 20140423

Available from: 2014-04-23 Created: 2014-04-22 Last updated: 2014-04-23Bibliographically approved

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Langmann, Edwin
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