Bose-Einstein condensation is macroscopic occupation of one or more eigenvectors of a Bose gas's one-particle density operator.
With trace normalized to the particle number 
, condensation in an orbital 
means that 
has a positive lower limit as the volume and particle number grow at
fixed density. On a periodic cube the constant orbital
is 
.
This occupation criterion concerns the many-body quantum
state, rather than merely the Bose-Einstein
distribution of an ideal gas.
Bose-Einstein Condensation
See also
Bose-Einstein Distribution, Bose Gas, Ground State, Partial Trace, Quantum DepletionExplore with Wolfram|Alpha
References
Lieb, E. H.; Seiringer, R.; Solovej, J. P.; and Yngvason, J. The Mathematics of the Bose Gas and Its Condensation. Basel, Switzerland: Birkhäuser, 2005. https://doi.org/10.1007/b137508.Cite this as:
Weisstein, Eric W. "Bose-Einstein Condensation." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/Bose-EinsteinCondensation.html