Duke Mathematical Journal

Generic Singular Spectrum For Ergodic Schrödinger Operators

Artur Avila and David Damanik

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We consider Schrödinger operators with ergodic potential $V_\omega(n)=f(T^{n}(\omega))$, $n \in \bb{Z}$, $\omega \in \Omega$, where $T:\Omega \to \Omega$ is a nonperiodic homeomorphism. We show that for generic $f \in C(\Omega)$, the spectrum has no absolutely continuous component. The proof is based on approximation by discontinuous potentials which can be treated via Kotani theory

Article information

Duke Math. J. Volume 130, Number 2 (2005), 393-400.

First available in Project Euclid: 15 November 2005

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 82B44: Disordered systems (random Ising models, random Schrödinger operators, etc.)
Secondary: 47B36: Jacobi (tridiagonal) operators (matrices) and generalizations


Avila, Artur; Damanik, David. Generic Singular Spectrum For Ergodic Schrödinger Operators. Duke Math. J. 130 (2005), no. 2, 393--400. doi:10.1215/S0012-7094-05-13035-6. http://projecteuclid.org/euclid.dmj/1132064631.

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