The dynamics of bose gases

We 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).

Name thesis:degree_name

Doctor of Philosophy

Level thesis:degree_level

Doctoral

Discipline thesis:degree_discipline

Mathematics

Grantor

The University of Texas at Austin

Year dc:date.issued

2015

Author dc:creator

• Taliaferro, Kenneth William

Advisor dc:contributor.advisor

• Chen, Thomas (Ph. D. in mechanical engineering and Ph. D. in mathematical physics)

Committee members dc:contributor.committeemember

• Maggi, Francesco
• Pavlovic, Natasa
• Tzirakis, Nikolaos
• Vasseur, Alexis

• Partial differential equations
• PDE
• Mathematical physics
• Gross-Pitaevskii hierarchy
• Bose gases
• Bosons
• Schrodinger equation
• Quantum mechanics

Language dc:language.iso

en

Identifier

doi:10.15781/T2459F

OAI identifier oai:identifier

oai:repositories.lib.utexas.edu:2152/31511