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

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

1999-09-13

arxiv.org/abs/hep-th/9909083v2

Prog.Theor.Phys.Suppl.134:171-181,1999

Physics

High Energy Physics

High Energy Physics - Theory

Based on the lecture given at 13th Nishinomiya-Yukawa Memorial Symposium on Dynamics of Fields and Strings, Nishinomiya, Japan

Scientific paper

10.1143/PTPS.134.171

I 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.

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