On the singular spectrum of the Almost Mathieu operator. Arithmetics and Cantor spectra of integrable models

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dc.creatorWiegmann, P. B.
dc.date1999-09-13
dc.date1999-09-15
dc.date.accessioned2026-07-07T11:10:35Z
dc.date.available2026-07-07T11:10:35Z
dc.descriptionI review a recent progress towards solution of the Almost Mathieu equation (A.G. Abanov, J.C. Talstra, P.B. Wiegmann, Nucl. Phys. B 525, 571, 1998), known also as Harper's equation or Azbel-Hofstadter problem. The spectrum of this equation is known to be a pure singular continuum with a rich hierarchical structure. Few years ago it has been found that the almost Mathieu operator is integrable. An asymptotic solution of this operator became possible due analysis the Bethe Ansatz equations.
dc.descriptionBased on the lecture given at 13th Nishinomiya-Yukawa Memorial Symposium on Dynamics of Fields and Strings, Nishinomiya, Japan, 12-13 Nov 1998, and talk given at YITP Workshop on New Aspects of Strings and Fields, Kyoto, Japan, 16-18 Nov 1998
dc.identifierhttps://arxiv.org/abs/hep-th/9909083
dc.identifierhttp://arxiv.org/abs/hep-th/9909083
dc.identifierProg.Theor.Phys.Suppl.134:171-181,1999
dc.identifierdoi:10.1143/PTPS.134.171
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/190820
dc.subjectHigh Energy Physics - Theory
dc.subjectAstrophysics
dc.subjectStrongly Correlated Electrons
dc.subjectExactly Solvable and Integrable Systems
dc.titleOn the singular spectrum of the Almost Mathieu operator. Arithmetics and Cantor spectra of integrable models
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