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On the Characteristic Polynomial of the Almost Mathieu Operator | Michael P. Lamoureux
; James A. Mingo
; | Date: |
20 Jun 2006 | Subject: | Operator Algebras | Abstract: | Let theta = p/q with p and q relatively prime and u and v a pair of unitaries such that u v = e^{i theta} v u, where u and v generate the rotation C*-algebra A_theta. Let h_{theta, lambda} = u + u^{-1} + lambda/2(v + v^{-1}) be the almost Mathieu operator. By proving an identity of rational functions we show that for q even, the constant term in the characteristic polynomial of h_{ heta, lambda} is (-1)^{q/2}(1 + (lambda/2)^q) - (z_1^q + z_1^{-q} + (lambda/2)^q(z_2^q + z_2^{-q})). | Source: | arXiv, math/0606507 | Services: | Forum | Review | PDF | Favorites |
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