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Thèse Année : 2010

Hunting colored (quantum) butterflies A geometric derivation of the TKNN-equations

Chasse aux papillons (quantiques) colorés : Une dérivation géométrique des équations TKNN

Giuseppe de Nittis
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Résumé

I consider the Hofstadter and the Harper operators, regarded as e ective models for a Bloch electron in a uniform magnetic eld, in the limit of weak and strong eld respectively. For each value of the Fermi energy in a spectral gap, I prove that the corresponding Fermi projectors exhibit a geometric duality, expressed in terms of some vector bundles canonically associated to the projectors. As a corollary, I get a rigorous geometric derivation of the TKNN equations. More generally, I prove that analogous equations hold true for any orthogonal projector in the rational rotation C -algebra, alias the algebra of the (rational) noncommutative torus.
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Dates et versions

tel-00674271 , version 1 (27-02-2012)

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  • HAL Id : tel-00674271 , version 1

Citer

Giuseppe de Nittis. Hunting colored (quantum) butterflies A geometric derivation of the TKNN-equations. Mathematical Physics [math-ph]. SISSA, Trieste, Italie, 2010. English. ⟨NNT : ⟩. ⟨tel-00674271⟩
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