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On the singular spectrum for adiabatic quasi-periodic Schrodinger operators on the real line

Alexander Fedotov·Frederic Klopp
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Abstract

In this paper, we study spectral properties of a family of quasi-periodic Schrodinger operators on the real line in the adiabatic limit. We assume that the adiabatic iso-energetic curves are extended along the momentum direction. In the energy intervals where this happens, we obtain an asymptotic formula for the Lyapunov exponent, and show that the spectrum is purely singular.

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Alexander Fedotov, Frederic Klopp. 2003-04-25. On the singular spectrum for adiabatic quasi-periodic Schrodinger operators on the real line. https://doi.org/10.1007/s00023-004-0186-4

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