Ground state and excited states of a trapped dilute condensed Bose gas

TL;DR

This paper reviews recent theoretical approaches to understanding the ground and excited states of a dilute Bose-Einstein condensate in a trap, extending classic results to trapped systems using the Gross-Pitaevskii and Bogoliubov formalisms.

Contribution

It generalizes Bogoliubov's uniform condensate results to trapped systems with the Gross-Pitaevskii and Bogoliubov equations, discussing recent studies and open questions.

Findings

Extension of Bogoliubov theory to trapped condensates

Discussion of linearized excitations in trapped systems

Identification of open research questions

Abstract

I review recent theoretical treatments of a dilute interacting condensed Bose gas in a trap. Bogoliubov's classic results for a uniform condensate are generalized to include the effect of a trap, using the Gross-Pitaevskii formalism (for the condensate) and the Bogoliubov equations (for the linearized small-amplitude excitations of the condensate). Several recent theoretical studies are discussed along with some open questions.