Theory of cold atoms: Bose-Einstein statistics

TL;DR

This paper provides a detailed tutorial on the mathematical techniques and theoretical description of Bose-Einstein statistics for cold atoms, including trapped Bose gases, emphasizing careful mathematical treatment to avoid misconceptions.

Contribution

It offers an in-depth, clarified mathematical framework for understanding Bose-Einstein statistics in cold atoms, especially for systems exhibiting Bose-Einstein condensation.

Findings

Clarifies mathematical techniques for Bose-Einstein statistics

Explains the theoretical description of trapped Bose atoms

Highlights common misconceptions and how to avoid them

Abstract

This Tutorial is the continuation of the previous tutorial part, published in Laser Phys. 23, 062001 (2013), where the basic mathematical techniques required for an accurate description of cold atoms for both types of quantum statistics are expounded. In the present part, the specifics of the correct theoretical description of atoms obeying Bose-Einstein statistics are explained, including trapped Bose atoms. In the theory of systems exhibiting the phenomenon of Bose-Einstein condensation, there exists a number of delicate mathematical points, whose misunderstanding often results in principally wrong conclusions. This is why the consideration in the present Tutorial is sufficiently detailed in order that the reader could clearly understand the underlying mathematics and would avoid confusions.