Title: WKB estimates and Harper’s operator as a dynamical system.
Abstract: We finish our discussion on the tight-binding reduction from Lecture 1, by deriving lower bounds on the tunneling coefficients which appear as overlap integrals in the tight-binding reduction and then discuss the leading-order approximation, Harper’s operator. We review the main features of this operator (metal-insulator transition and Cantor spectrum for incommensurable flux) with an emphasis on the localized regime (positive Lyapunov exponent).
Bryna Kra
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