Approximate spectral theory and wave propagation in quasi-periodic media
Antoine Benoît, Mitia Duerinckx, Antoine Gloria, Christopher Shirley · Journées Équations aux dérivées partielles · 2018
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).