Singular Continuous Spectrum for the Period Doubling Hamiltonian on a Set of Full Measure

Abstract:We consider the discrete one-dimensional Schrödinger operator with potential generated by the period doubling substitution. We show that for almost every element in the hull Ο, with respect to the unique ergodic measure μ on Ο, there are no eigenvalues. Combining this with a result proven by Kotani, we establish purely singular continuous spectrum on a set of full measure.

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