JournalsjemsVol. 21, No. 3pp. 777–795

All couplings localization for quasiperiodic operators with monotone potentials

  • Svetlana Jitomirskaya

    University of California, Irvine, USA
  • Ilya Kachkovskiy

    Michigan State University, East Lansing, USA
All couplings localization for quasiperiodic operators with monotone potentials cover

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Abstract

We establish Anderson localization for quasiperiodic operator families of the form

(H(x)ψ)(m)=ψ(m+1)+ψ(m1)+λv(x+mα)ψ(m)(H(x)\psi)(m)=\psi(m+1)+\psi(m-1)+\lambda v(x+m\alpha)\psi(m)

for all coupling constants λ>0\lambda > 0 and all Diophantine frequencies α\alpha, provided that vv is a 1-periodic function satisfying a Lipschitz monotonicity condition on [0,1). The localization is uniform on any energy interval on which the Lyapunov exponent is bounded from below.

Cite this article

Svetlana Jitomirskaya, Ilya Kachkovskiy, All couplings localization for quasiperiodic operators with monotone potentials. J. Eur. Math. Soc. 21 (2018), no. 3, pp. 777–795

DOI 10.4171/JEMS/850