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Please use this identifier to cite or link to this item: http://hdl.handle.net/2289/2661
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dc.contributor.authorShastry, Sriram B.-
dc.contributor.authorDhar, Abhishek-
dc.date.accessioned2007-06-11T06:16:14Z-
dc.date.available2007-06-11T06:16:14Z-
dc.date.issued2001-08-
dc.identifier.citationJournal of Physics A, 2001, Vol.34, p6197-6208en
dc.identifier.issn1751-8113-
dc.identifier.issn1751-8121 (Online)-
dc.identifier.urihttp://hdl.handle.net/2289/2661-
dc.descriptionRestricted Access. An open-access version is available at arXiv.org (one of the alternative locations)en
dc.description.abstractWe present the exact solution for a set of nonlinear algebraic equations 1/zl = πd + (2d/n)∑m≠l1/(zl-zm). These were encountered by us in a recent study of the low-energy spectrum of the Heisenberg ferromagnetic chain. These equations are low-d (density) `degenerations' of a more complicated transcendental equation of Bethe's ansatz for a ferromagnet, but are interesting in themselves. They generalize, through a single parameter, the equations of Stieltjes, xl = ∑m≠l1/(xl-xm), familiar from random matrix theory. It is shown that the solutions of these set of equations are given by the zeros of generalized associated Laguerre polynomials. These zeros are interesting, since they provide one of the few known cases where the location is along a nontrivial curve in the complex plane that is determined in this work. Using a `Green function' and a saddle point technique we determine the asymptotic distribution of zeros.en
dc.format.extent149536 bytes-
dc.format.mimetypeapplication/pdf-
dc.language.isoenen
dc.publisherIOP Publishing Ltd.en
dc.relation.urihttp://arxiv.org/abs/cond-mat/0101464en
dc.relation.urihttp://dx.doi.org/:10.1088/0305-4470/34/31/313en
dc.rights2001 IOP Publishing Ltd.en
dc.titleSolution of a generalized Stieltjes problemen
dc.typeArticleen
Appears in Collections:Research Papers (TP)

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