Abstract
We prove long time Anderson localization for the nonlinear random Schrödinger equation for arbitrary ℓ 2 initial data, hence giving an answer to a widely debated question in the physics community. The proof uses a Birkhoff normal form type transform to create a barrier where there is essentially no propagation. One of the new features is that this transform is in a small neighborhood enabling us to treat “rough” data, where there are no moment conditions. The formulation of the present result is inspired by the RAGE theorem.
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To J. Fröhlich and T. Spencer on their sixtieth birthdays.
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Wang, WM., Zhang, Z. Long Time Anderson Localization for the Nonlinear Random Schrödinger Equation. J Stat Phys 134, 953–968 (2009). https://doi.org/10.1007/s10955-008-9649-1
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DOI: https://doi.org/10.1007/s10955-008-9649-1