Abstract
In this article we make specific in the quasi-periodic setting the general Floquet-Bloch theory we have introduced for stationary ergodic operators together with the associated approximate spectral theory. As an application we consider the long-time behavior of the Schrödinger flow with a quasi-periodic potential (in the regime of small intensity of the discorder), and the long-time behavior of the wave equation with quasi-periodic coefficients (in the homogenization regime).
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