Many-Body Boson Systems pp 43-107 | Cite as

# Bose Einstein Condensation (BEC)

## Abstract

Bose (1924) and Einstein (1925) considered a finite but arbitrary large set of what they called Planck oscillators and applied statistics to it. They pointed out the possibility of an arbitrary large number of oscillators to be in a zero momentum state. This property was interpreted as a physical phenomenon, a kind of condensation phenomenon. Later when second quantization was formulated, the oscillators where called boson particles. This was the birth of the famous *Bose-Einstein Condensation*, nowadays denoted in short by BEC. This work of Bose and Einstein garnered considerable discussion for more than a decade, particularly in clarifying the meaning behind the appearance of phase transitions in finite systems. In 1938 London (1938) introduced the concept of macroscopic occupation of the ground state and related it to the long range coherence properties of the Bose-Einstein condensate. Since that period, the physics of the phenomenon has become standard knowledge in statistical mechanics and present in all related textbooks. Each assembly of many free boson particles shows condensation, namely a macroscopic number of the bosons in the momentum (*p*=0)-mode, if the density is large enough or if the temperature is low enough. It is fundamentally a pure quantum phenomenon, as it holds even for a system of free quantum particles and because it disappears in the classical limit.

## Keywords

Thermodynamic Limit Bose Einstein Condensation Boson System Ergodic State Condensate Density## Preview

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## References

- 24.Bose S.N.:
*Planck’s Gezetz und Lichtquantenhypothese*, Z. Phys.**26**, 178–181 (1924) CrossRefGoogle Scholar - 42.Einstein A.:
*Quantentheorie des einatomigen idealen gases*, Sitzungber. Preuss.**9**, 3–14 (1925) Google Scholar - 108.London F.:
*On the Bose-Einstein condensation*, Phys. Rev.**54**, 947–954 (1938) MATHCrossRefGoogle Scholar