Persistent Link:
http://hdl.handle.net/10150/185541
Title:
Wave scattering in random media.
Author:
Tsay, Jhishen.
Issue Date:
1991
Publisher:
The University of Arizona.
Rights:
Copyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.
Abstract:
We study the scattering theory for the descrete Schrodinger equation with a random potential having large finite support. We consider in one dimension a wave packet incoming from one side of the disordered section. We prove that the transmission of a wave packet is improbable if the disordered section is large, and that a fluctuation deep within the disordered section has a very small effect on the scattering of wave packets. The scattering theory for the discrete random Schrodinger equation in a strip in two dimensions is also considered. We derive large deviation bounds on the elements of the transmission matrix uniform in the energy parameter. These uniform bounds are used to show that the probability of a significant portion of a wave packet is transmitted is small as the length of the disordered section becomes large. We also study the time delay in potential scattering. We consider the situation when the potential becomes a white noise. The time delay is related to the energy derivative of the phase shift. We derive stochastic differential equations for the phase shift and the frequency derivative of the phase shift. We find that there is no time delay in the low frequency limit. However in the high frequency limit we find the time delay is a random function of the depth of the disordered section.
Type:
text; Dissertation-Reproduction (electronic)
Keywords:
Dissertations, Academic; Mathematics.
Degree Name:
Ph.D.
Degree Level:
doctoral
Degree Program:
Applied Mathematics; Graduate College
Degree Grantor:
University of Arizona
Advisor:
Faris, William G.

Full metadata record

DC FieldValue Language
dc.language.isoenen_US
dc.titleWave scattering in random media.en_US
dc.creatorTsay, Jhishen.en_US
dc.contributor.authorTsay, Jhishen.en_US
dc.date.issued1991en_US
dc.publisherThe University of Arizona.en_US
dc.rightsCopyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.en_US
dc.description.abstractWe study the scattering theory for the descrete Schrodinger equation with a random potential having large finite support. We consider in one dimension a wave packet incoming from one side of the disordered section. We prove that the transmission of a wave packet is improbable if the disordered section is large, and that a fluctuation deep within the disordered section has a very small effect on the scattering of wave packets. The scattering theory for the discrete random Schrodinger equation in a strip in two dimensions is also considered. We derive large deviation bounds on the elements of the transmission matrix uniform in the energy parameter. These uniform bounds are used to show that the probability of a significant portion of a wave packet is transmitted is small as the length of the disordered section becomes large. We also study the time delay in potential scattering. We consider the situation when the potential becomes a white noise. The time delay is related to the energy derivative of the phase shift. We derive stochastic differential equations for the phase shift and the frequency derivative of the phase shift. We find that there is no time delay in the low frequency limit. However in the high frequency limit we find the time delay is a random function of the depth of the disordered section.en_US
dc.typetexten_US
dc.typeDissertation-Reproduction (electronic)en_US
dc.subjectDissertations, Academicen_US
dc.subjectMathematics.en_US
thesis.degree.namePh.D.en_US
thesis.degree.leveldoctoralen_US
thesis.degree.disciplineApplied Mathematicsen_US
thesis.degree.disciplineGraduate Collegeen_US
thesis.degree.grantorUniversity of Arizonaen_US
dc.contributor.advisorFaris, William G.en_US
dc.contributor.committeememberBayly, Bruce J.en_US
dc.contributor.committeememberKennedy, Thomas G.en_US
dc.contributor.committeememberMaier, Robert S.en_US
dc.identifier.proquest9136870en_US
dc.identifier.oclc711690153en_US
All Items in UA Campus Repository are protected by copyright, with all rights reserved, unless otherwise indicated.