Journal of the European Mathematical Society
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Published online: 2018-11-26
All couplings localization for quasiperiodic operators with monotone potentialsSvetlana Jitomirskaya and Ilya Kachkovskiy (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