Ideal Bose Gas

A Bose–Einstein condensate (BEC) is a state of matter of a dilute gas of bosons cooled to temperatures very close to 0K (usually ~100nK in experiments). Under such conditions, a large fraction of bosons occupies the lowest quantum state, at which point macroscopic quantum phenomena become apparent.

Overview

In this section, we summarize some basic and useful thermodynamic results for Bose-Einstein condensation in a uniform, non-interacting gas of bosons.

Thermodynamics of a Bose Gas

The Bose Distribution

For non-interacting bosons in thermodynamic equilibrium, the mean occupation number of the single-particle state $\nu$ is

$\langle n_{\nu }\rangle ={\frac {1}{e^{(\epsilon _{\nu }-\mu )/kT}-1}}\,.$

In a classical gas, the mean occupation number for a single quantum state satisfies the Boltzmann distribution $\langle n_{\nu }\rangle =e^{-(\epsilon _{\nu }-\mu )/kT}$ which is much less than unity. However, in a condesnate, the occupatyion number in the groud state is much larger than 1.