All couplings localization for quasiperiodic operators with Lipschitz monotone potentials

Svetlana Jitomirskaya; Ilya Kachkovskiy

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arXiv · 1509.02226

All couplings localization for quasiperiodic operators with Lipschitz monotone potentials

Svetlana Jitomirskaya·Ilya Kachkovskiy

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Abstract

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 $\lambda>0$ and all Diophantine $\alpha$, 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 Lyapunov exponent is bounded from below.

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BibTeX RIS

Svetlana Jitomirskaya, Ilya Kachkovskiy. 2015-09-07. All couplings localization for quasiperiodic operators with Lipschitz monotone potentials. https://arxiv.org/abs/1509.02226

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