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Absolutely continuous convolutions of singular measures and an application to the square Fibonacci Hamiltonian. (English) Zbl 1358.37117

Summary: We prove for the square Fibonacci Hamiltonian that the density of states measure is absolutely continuous for almost all pairs of small coupling constants. This is obtained from a new result we establish about the absolute continuity of convolutions of measures arising in hyperbolic dynamics with exact-dimensional measures.

MSC:

37N20 Dynamical systems in other branches of physics (quantum mechanics, general relativity, laser physics)
47N50 Applications of operator theory in the physical sciences
81Q10 Selfadjoint operator theory in quantum theory, including spectral analysis
37C45 Dimension theory of smooth dynamical systems
47B36 Jacobi (tridiagonal) operators (matrices) and generalizations
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References:

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