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A Lower Bound on the Lyapunov Exponent for the Generalized Harper’s Model

Abstract

We obtain a lower bound for the Lyapunov exponent of a family of discrete Schrödinger operators \((Hu)_n=u_{n+1}+u_{n-1}+2a_1\cos 2\pi (\theta +n\alpha )u_n+2a_2\cos 4\pi (\theta +n\alpha )u_n\), that incorporates both \(a_1\) and \(a_2,\) thus going beyond the Herman’s bound.

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Acknowledgments

S. J. is a 2014–2015 Simons Fellow. This research was partially supported by NSF DMS-1401204.

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Correspondence to Svetlana Jitomirskaya.

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Dedicated to David Ruelle and Yasha Sinai on the occasion of their 80th birthdays.

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Jitomirskaya, S., Liu, W. A Lower Bound on the Lyapunov Exponent for the Generalized Harper’s Model. J Stat Phys 166, 609–617 (2017). https://doi.org/10.1007/s10955-016-1543-7

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  • DOI: https://doi.org/10.1007/s10955-016-1543-7

Keywords

  • Lyapunov exponents
  • Quasiperiodic
  • Generalized Harper’s