The dynamics of bose gases

dc.contributor.advisorChen, Thomas (Ph. D. in mechanical engineering and Ph. D. in mathematical physics)en
dc.contributor.committeeMemberMaggi, Francescoen
dc.contributor.committeeMemberPavlovic, Natasaen
dc.contributor.committeeMemberTzirakis, Nikolaosen
dc.contributor.committeeMemberVasseur, Alexisen
dc.creatorTaliaferro, Kenneth Williamen
dc.creator.orcid0000-0002-6441-921Xen
dc.date.accessioned2015-10-02T19:02:55Zen
dc.date.available2015-10-02T19:02:55Zen
dc.date.issued2015-05en
dc.date.submittedMay 2015en
dc.date.updated2015-10-02T19:02:55Zen
dc.descriptiontexten
dc.description.abstractWe study the Gross-Pitaevskii (GP) hierarchy, which is an infinite sequence of coupled partial differential equations that models the dynamics of Bose gases and arises in the derivation of the cubic and quintic nonlinear Schrödinger equations from an N-body linear Schrödinger equation. In Chapter 2, we consider the cubic case in R³ and derive the GP hierarchy in the strong topology corresponding to the spaces used by Klainerman and Machedon in (82). We also prove that positive semidefiniteness of solutions is preserved over time and use this result to prove global well-posedness of solutions to the GP hierarchy. This is based on a joint work with Thomas Chen (24). In Chapters 3 and 4, we prove uniqueness of solutions to the GP hierarchy in R[superscript d] in a low regularity Sobolev type space in the cubic and quintic cases, respectively. These chapters are an extension of the work of Chen-Hainzl-Pavlović-Seiringer (17) and are based on joint works with Younghun Hong and Zhihui Xie (70,71).en
dc.description.departmentMathematicsen
dc.format.mimetypeapplication/pdfen
dc.identifierdoi:10.15781/T2459Fen
dc.identifier.urihttp://hdl.handle.net/2152/31511en
dc.language.isoenen
dc.subjectPartial differential equationsen
dc.subjectPDEen
dc.subjectMathematical physicsen
dc.subjectGross-Pitaevskii hierarchyen
dc.subjectBose gasesen
dc.subjectBosonsen
dc.subjectSchrodinger equationen
dc.subjectQuantum mechanicsen
dc.titleThe dynamics of bose gasesen
dc.typeThesisen
thesis.degree.departmentMathematicsen
thesis.degree.disciplineMathematicsen
thesis.degree.grantorThe University of Texas at Austinen
thesis.degree.levelDoctoralen
thesis.degree.nameDoctor of Philosophyen
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