Measures of Fermi surfaces and absence of singular continuous spectrum for magnetic Schroedinger operators

Details Measures of Fermi surfaces and absence of singular continuous spectrum for magnetic Schroedinger operators Measures of Fermi surfaces and absence of singular continuous spectrum for magnetic Schroedinger operators

1999-08-25

arxiv.org/abs/math-ph/9908026v1

Math. Nachr. 233-234 (2002), 111-127

Physics

Mathematical Physics

19 pages

Scientific paper

10.1002/1522-2616(200201)233:1<1

Fermi surfaces are basic objects in solid state physics and in the spectral theory of periodic operators. We define several measures connected to Fermi surfaces and study their measure theoretic properties. From this we get absence of singular continuous spectrum and of singular continuous components in the density of states for symmetric periodic elliptic differential operators acting on vector bundles. This includes Schroedinger operators with periodic magnetic field and rational flux, as well as the corresponding Pauli and Dirac-type operators.

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