The Mathematics of the Bose Gas and its Condensation

TL;DR

This book provides a rigorous mathematical overview of the quantum many-body problem of the Bose gas, covering topics like Bose-Einstein condensation and superfluidity, with relevance to ultra-cold gas experiments.

Contribution

It offers a comprehensive, mathematically rigorous survey of recent results on the Bose gas, including new analytic techniques and insights into phenomena like condensation and superfluidity.

Findings

Analysis of ground state energy and the Gross-Pitaevskii equation

Mathematical proof of Bose-Einstein condensation

Insights into superfluidity and rotating gases

Abstract

This book surveys results about the quantum mechanical many-body problem of the Bose gas that have been obtained by the authors over the last seven years. These topics are relevant to current experiments on ultra-cold gases; they are also mathematically rigorous, using many analytic techniques developed over the years to handle such problems. Some of the topics treated are the ground state energy, the Gross-Pitaevskii equation, Bose-Einstein condensation, superfluidity, one-dimensional gases, and rotating gases. The book also provides a pedagogical entry into the field for graduate students and researchers.