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On Optimal Separation of Eigenvalues for a Quasiperiodic Jacobi Matrix

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Abstract

We consider quasiperiodic Jacobi matrices of size N with analytic coefficients. We show that, in the positive Lyapunov exponent regime, after removing some small sets of energies and frequencies, any eigenvalue is separated from the rest of the spectrum by N −1(log N)−p, with p > 15.

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Authors and Affiliations

  1. Department of Mathematics, University of Toronto, Toronto, ON, M5S 2E4, Canada

    Ilia Binder & Mircea Voda

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  1. Ilia Binder
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  2. Mircea Voda
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Correspondence to Mircea Voda.

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Communicated by W. Schlag

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Binder, I., Voda, M. On Optimal Separation of Eigenvalues for a Quasiperiodic Jacobi Matrix. Commun. Math. Phys. 325, 1063–1106 (2014). https://doi.org/10.1007/s00220-013-1836-5

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  • DOI: https://doi.org/10.1007/s00220-013-1836-5

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