Bose-Einstein Distribution Function

An orbital can support any number of bosons, which fundamentally changes the Gibbs Sum and thus the distribution function. Instead of summing over N = 0, 1 we must sum over all N. The final result is:

f () =

Einstein Condensation

Since there is no restriction on the number of particles in the ground state, a low enough temperature would deny the system of the thermal excitation required to promote very many bosons out of the lowest energy orbital.

There is, then, a transition temperature below which the lowest energy "ground" orbital possesses a large number of bosons. Above this temperature, entropy and thermal excitation render the ground orbital sparsely populated. This transition temperature is known as the Einstein condensation temperature, and the effect of bosons crowding the ground orbital is known as the Einstein condensation.

The Einstein condensation temperature is given by:


The most common condensate is liquid Helium. The crowding is so profound that one can actually see macroscopically the ground orbital of a Helium liquid with the proper equipment. Physics such as superfluidity are also outgrowths of the study of this condensation.