Mathematical Analysis of Interacting Bose Gases

Princeton University, Princeton NJ

Investigators

Abstract

Mathematical Analysis of Interacting Bose Gases" by R. Seiringer The main focus of this project is the continuation of the author's research in the mathematical analysis of the low-temperature properties of an interacting Bose gas, with special attention on the phenomenon of Bose-Einstein condensation. Motivated by recent experimental breakthroughs in the treatment of dilute Bose gases, which led to Nobel prize awards in 2001, there has been a lot of progress in this field in the last few years. Partly in joint work with E.H. Lieb and J. Yngvason it was possible to rigorously prove the existence of Bose-Einstein condensation, superfluidity and other phenomena like one-dimensional behavior of trapped gases in highly elongated traps, starting from the basic Schroedinger equation. With the help of developing the necessary mathematical tools it was possible to gain considerable physical insight into these phenomena. There are a lot of open problems, however, that are planned to be addressed within this project. Among them are the proof of Bose-Einstein condensation for infinite (in contrast to trapped) systems, behavior of rotating systems and vortices, mixtures of Bose and Fermi gases, etc. These problems are interesting both from a mathematical and physical point of view, being of a complex nature that brings about the need for new mathematical ideas, and being closely related to properties of systems studied for the first time in current experiments which can be expected to yield further fascinating results within the near future. Progress in the mathematical analysis of these phenomena will certainly yield further insight into the complex physics that is going on in interacting bosonic systems at very low temperature. Other fields of research that the author would like to study within this project include the Pauli-Fierz model of non-relativistic Quantum Electro-dynamics, the Bessis-Moussa-Villani conjecture about traces of positive matrices, and classical models of Quark confinement.