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Journal of the European Mathematical Society


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Volume 21, Issue 3, 2019, pp. 777–795
DOI: 10.4171/JEMS/850

Published online: 2018-11-26

All couplings localization for quasiperiodic operators with monotone potentials

Svetlana Jitomirskaya[1] and Ilya Kachkovskiy[2]

(1) University of California, Irvine, USA
(2) Michigan State University, East Lansing, USA

We establish Anderson localization for quasiperiodic operator families of the form $$(H(x)\psi)(m)=\psi(m+1)+\psi(m-1)+\lambda v(x+m\alpha)\psi(m)$$ for all coupling constants $\lambda > 0$ and all Diophantine frequencies $\alpha$, provided that $v$ 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.

Keywords: Anderson localization, quasiperiodic Schrödinger operator, purely point spectrum

Jitomirskaya Svetlana, Kachkovskiy Ilya: All couplings localization for quasiperiodic operators with monotone potentials. J. Eur. Math. Soc. 21 (2019), 777-795. doi: 10.4171/JEMS/850