We prove long time Anderson localization for the nonlinear random Schroedinger equation, giving an answer to a widely debated question in the physics community. I will conjecture Arnold type diffusion in the infinite time limit, which is also supported by my work on the time dependent linear Schroedinger equation on the circle.
A seminar from the Classical and Quantum Transport in the Presence of Disorder conference in association with the Newton Institute programme: Mathematics and Physics of Anderson localization: 50 Years After
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