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Structure and dynamics of noncommutative solitons
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Krueger, August John. Structure and dynamics of noncommutative solitons. Retrieved from https://doi.org/doi:10.7282/T3765CS3

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TitleStructure and dynamics of noncommutative solitons
NameKrueger, August John (author); Soffer, Avraham (chair); Lebowitz, Joel (co-chair); Goldstein, Sheldon (internal member); Shapiro, Joel (internal member); Tahvildar-Zadeh, A. Shadi (outside member); Rutgers University; Graduate School - New Brunswick
Date Created2014
Other Date2014-10 (degree)
SubjectPhysics and Astronomy, Noncommutative differential geometry, Spectral theory (Mathematics)
Extent1 online resource (vii, 83 p. : ill.)
DescriptionWe consider the Schrödinger equation with a Hamiltonian given by a second order o difference operator with nonconstant growing coefficients, on the half one dimensional lattice. This operator appeared first naturally in the construction and dynamics of noncommutative solitons in the context of noncommutative field theory. We prove pointwise in time decay estimates, with the optimal decay rate t−1 log−2 t generically. We use a novel technique involving generating functions of orthogonal polynomials to achieve these estimates. We construct a ground state soliton for this equation and analyze its properties. In particular we arrive at ∞ and 1 estimates as well as a quasi-exponential spatial decay rate. We completely determine the spectrum of the associated linearized Hamiltonian and prove the optimal decay rate of t−1 log−2 t for the associated time decay estimate. These results are to appear in forthcoming papers
NotePh.D.
NoteIncludes bibliographical references
Noteby August John Krueger
Genretheses, ETD doctoral
Persistent URLhttps://doi.org/doi:10.7282/T3765CS3
Languageeng
CollectionGraduate School - New Brunswick Electronic Theses and Dissertations
Organization NameRutgers, The State University of New Jersey
RightsThe author owns the copyright to this work.
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