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Type of Document	Dissertation
Author	Cai, Kaihua
Author's Email Address	kaihua AT caltech.edu
URN	etd-06022005-153453
Persistent URL	http://resolver.caltech.edu/CaltechETD:etd-06022005-153453
Title	Dispersive properties of Schrodinger equations
Degree	PhD
Option	Mathematics
Advisory Committee	Advisor Name Title Wilhelm Schlag Committee Chair Malabika Pramanik Committee Member Michael Goldberg Committee Member Rowan Killip Committee Member
Keywords	Schrodinger Dispersive
Date of Defense	2005-05-19
Availability	unrestricted
Abstract This thesis mainly concerns the dispersive properties of Schrodinger equations with certain potentials, and some of their consequences. First, we consider the charge transfer models in R^n with n > 2. In this case, the potential is a sum of several individual real-valued potentials, each moving with constant velocities. We get an L^1 to L^infty estimate for the evolution and the asymptotic completeness of the evoution in any Sobolev space. Second, we derive the L^1 to L^infty estimate for the Schrodinger operators with a Lame potential. The Lame potential is spatially periodic and its spectrum has the structure of finite bands. We obtain a dispersive estimate with a decay rate t^{-1/3}.
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