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Metal-insulator transition for the almost Mathieu operator
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We prove that for Diophantine \om and almost every \th, the almost Mathieu operator, (H_{\omega,\lambda,\theta}\Psi)(n)=\Psi(n+1) + \Psi(n-1) + \lambda\cos 2\pi(\omega n +\theta)\Psi(n), exhibits localization for \lambda > 2 and purely absolutely continuous spectrum for \lambda < 2. This completes the proof of (a correct version of) the Aubry-Andr\'e conjecture.
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Cited by 3 Pith papers
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Observation of Metal-Insulator and Spectral Phase Transitions in Aubry-Andr\'e-Harper Models
A single-photon quantum-walk experiment realizes the unitary almost-Mathieu operator and observes metal-insulator, parity-time symmetry-breaking, and all-imaginary-quasienergy spectral transitions.
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