Bose-Einstein condensation in real space

TL;DR

This paper explains how Bose-Einstein condensation can occur in real space, highlighting differences from classical gases and emphasizing the role of particle size in the condensate phase.

Contribution

It introduces the concept of Bose-Einstein condensation in real space and compares it to van der Waals gases, emphasizing the significance of particle size.

Findings

Bose-Einstein condensation occurs in real space.

Volume per particle can reach zero in the condensate phase.

Differences between ideal Bose gas and van der Waals gas are clarified.

Abstract

We illustrate how Bose-Einstein condensation occurs not only in momentum space but also in coordinate (or real) space. Analogies between the isotherms of a van der Waals gas of extended (or finite-diameter) identical atoms and the point (or zero-diameter) particles of an ideal Bose gas allow one to conclude that, in contrast to the van der Waals case, the volume per particle can go to zero in the pure Bose condensate phase precisely because the particle diameter is zero.