Long-time Anderson Localization for the Nonlinear quasi-periodic Schr\"odinger Equation on $\mathbb Z^d$

Abstract

Using a Birkhoff normal form transform to impede mode transfer in a finite "barrier", we prove localization of arbitrary $\ell^2$ data for polynomially long time for the nonlinear quasi-periodic Schr\"odinger equation on $\mathbb Z^d$.