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dc.contributor.advisorKuchment, Peter
dc.creatorDo, Ngoc Thanh
dc.date.accessioned2016-09-22T19:40:21Z
dc.date.available2016-09-22T19:40:21Z
dc.date.created2016-08
dc.date.issued2016-05-31
dc.date.submittedAugust 2016
dc.identifier.urihttp://hdl.handle.net/1969.1/157943
dc.description.abstractIn this dissertation we deal with some spectral problems for periodic differential operators originating from mathematical physics. We begin by using quantum graphs to model a particular graphyne and related nanotubes. The dispersion relations, and thus spectra, of periodic Schrödinger operators on these structures are analyzed. We find highly directional Dirac cones, which makes some types of graphynes fascinating. Then, we study a conjecture that has been widely assumed in solid state physics. Namely, the extrema of the dispersion relation of a generic periodic difference operator on a class of discrete graphs are proven to be non-degenerate. Here, by non-degeneracy we mean extrema having non-degenerate Hessian. Finally, we present a technique of creating and manipulating spectral gaps for a (regular) periodic quantum graph by inserting appropriate internal structures into its vertices.en
dc.format.mimetypeapplication/pdf
dc.language.isoen
dc.subjectMathematical physicsen
dc.subjectspectral theoryen
dc.subjectperiodic differential equationsen
dc.subjectSchrodinger equationen
dc.subjectgraphyneen
dc.subjectcarbon nanotubesen
dc.subjectspectral gapen
dc.subjectdispersion relationen
dc.titleSome Spectral Problems in Mathematical Physicsen
dc.typeThesisen
thesis.degree.departmentMathematicsen
thesis.degree.disciplineMathematicsen
thesis.degree.grantorTexas A & M Universityen
thesis.degree.nameDoctor of Philosophyen
thesis.degree.levelDoctoralen
dc.contributor.committeeMemberAbanov, Artem
dc.contributor.committeeMemberBerkolaiko, Gregory
dc.contributor.committeeMemberWard, Joseph
dc.type.materialtexten
dc.date.updated2016-09-22T19:40:21Z
local.etdauthor.orcid0000-0002-5761-3946


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