BEC

BEC usually means Bose–Einstein condensate or Bose–Einstein condensation. It refers to macroscopic occupation of a single quantum state or mode by bosons under suitable thermodynamic conditions.

Formula Hook

For a uniform ideal Bose gas in three dimensions, condensation occurs when the phase-space density reaches the scale

$$n\lambda_T^3 \gtrsim \zeta(3/2),$$

where $n$ is number density and $\lambda_T$ is the thermal de Broglie wavelength. In the ideal gas below the critical temperature,

$$\frac{N_0}{N} = 1- \left( \frac{T}{T_c} \right)^{3/2}.$$

Real trapped and interacting condensates require additional modeling.

Canonical Route

This acronym entry is the compact BEC lookup home. The canonical many-body treatment is Bose–Einstein Condensation. For foundations, see Bosons, Bosonic Fock Space, and Math Needed for Many-Body QM.

Common Confusions

• BEC is not the definition of a boson; it is a many-body thermodynamic phenomenon available to some bosonic systems.
• Condensation and superfluidity are related in many systems but are not identical concepts.
• Finite traps, interactions, dimensionality, and disorder change the ideal-gas formula.

References

• S. N. Bose, “Plancks Gesetz und Lichtquantenhypothese,” Zeitschrift fuer Physik 26, 178-181, 1924.
• A. Einstein, “Quantentheorie des einatomigen idealen Gases,” Sitzungsberichte der Preussischen Akademie der Wissenschaften, 1924.
• C. J. Pethick and H. Smith, Bose-Einstein Condensation in Dilute Gases, 2nd ed., Cambridge University Press, 2008.