Bose-Einstein statistics

Bose–Einstein statistics is the counting rule for a collection of identical bosons sharing the available energy states. Unlike fermions, bosons face no exclusion: any number of them can occupy the very same state, and there is no ceiling. When you work out how a crowd of bosons settles in thermal equilibrium, this freedom to pile up leads to occupation numbers that classical counting would never predict.

The rule is summed up by the Bose–Einstein distribution, giving the average number of bosons in a state of a given energy and temperature. For low-energy states this number can grow very large, reflecting the bosons' tendency to congregate. The symmetric exchange behaviour of bosons makes a state already holding many particles even more attractive to the next one — a kind of quantum gregariousness with no classical analogue.

Developed when Satyendra Nath Bose's counting of photons was extended to atoms by Albert Einstein in the mid-1920s, these statistics explain the spectrum of light from a hot body, the workings of the laser, and the friction-free flow of a superfluid. Their most spectacular prediction is that, cooled enough, a gas of bosons can dump a macroscopic fraction of its particles into a single lowest state — the Bose–Einstein condensate.