Dispersive Properties of Schrödinger Equations

Citation

Cai, Kaihua (2005) Dispersive Properties of Schrödinger Equations. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/EGNB-FZ41. https://resolver.caltech.edu/CaltechETD:etd-06022005-153453

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 Rⁿ 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 L¹ to L^∞ estimate for the evolution and the asymptotic completeness of the evolution in any Sobolev space.

Second, we derive the L¹ to L^∞ 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.

Item Type:	Thesis (Dissertation (Ph.D.))
Subject Keywords:	Dispersive; Schrodinger
Degree Grantor:	California Institute of Technology
Division:	Physics, Mathematics and Astronomy
Major Option:	Mathematics
Thesis Availability:	Public (worldwide access)
Research Advisor(s):	Schlag, Wilhelm
Thesis Committee:	Schlag, Wilhelm (chair) Pramanik, Malabika Goldberg, Michael Killip, Rowan
Defense Date:	19 May 2005
Record Number:	CaltechETD:etd-06022005-153453
Persistent URL:	https://resolver.caltech.edu/CaltechETD:etd-06022005-153453
DOI:	10.7907/EGNB-FZ41
Default Usage Policy:	No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:	2392
Collection:	CaltechTHESIS
Deposited By:	Imported from ETD-db
Deposited On:	03 Jun 2005
Last Modified:	10 Dec 2020 20:16

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