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

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

2003-04-25

arxiv.org/abs/math-ph/0304035v1

Physics

Mathematical Physics

Scientific paper

10.1007/s00023-004-0186-4

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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