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Full-Text Articles in Physical Sciences and Mathematics
The Schroedinger Equation With Potential In Random Motion, Marius Beceanu, Soffer Avy
The Schroedinger Equation With Potential In Random Motion, Marius Beceanu, Soffer Avy
Mathematics and Statistics Faculty Scholarship
We study Schroedinger's equation with a potential moving along a Brownian motion path. We prove a RAGE-type theorem and Strichartz estimates for the solution on average.
The Schroedinger Equation With Potential In Rough Motion, Marius Beceanu, Avy Soffer
The Schroedinger Equation With Potential In Rough Motion, Marius Beceanu, Avy Soffer
Mathematics and Statistics Faculty Scholarship
This paper proves endpoint Strichartz estimates for the linear Schroedinger equation in R 3 , with a time-dependent potential that keeps a constant profile and is subject to a rough motion, which need not be differentiable and may be large in norm. The potential is also subjected to a time-dependent rescaling, with a non-differentiable dilation parameter. We use the Strichartz estimates to prove the non-dispersion of bound states, when the path is small in norm, as well as boundedness of energy. We also include a sample nonlinear application of the linear results.