Nonlinear Anderson Localized States at Arbitrary Disorder

Given an Anderson model H = - Δ + V in arbitrary dimensions, and assuming the model satisfies localization, we construct quasi-periodic in time (and localized in space) solutions for the nonlinear random Schrödinger equation i ∂ u ∂ t = - Δ u + V u + δ | u | 2 p u for small δ . Our approach combines...

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Bibliographic Details
Published in:Communications in mathematical physics 2024-11, Vol.405 (11), Article 272
Main Authors: Liu, Wencai, Wang, W.-M.
Format: Article
Language:English
Subjects:
Classical and Quantum Gravitation
Complex Systems
Mathematical and Computational Physics
Mathematical Physics
Nonlinear differential equations
Parabolic differential equations
Partial differential equations
Physics
Physics and Astronomy
Quantum Physics
Relativity Theory
Schrodinger equation
Theoretical
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Summary:Given an Anderson model H = - Δ + V in arbitrary dimensions, and assuming the model satisfies localization, we construct quasi-periodic in time (and localized in space) solutions for the nonlinear random Schrödinger equation i ∂ u ∂ t = - Δ u + V u + δ | u | 2 p u for small δ . Our approach combines probabilistic estimates from the Anderson model with the Craig–Wayne–Bourgain method for studying quasi-periodic solutions of nonlinear PDEs.
ISSN:0010-3616
1432-0916
DOI:10.1007/s00220-024-05150-z