# Cases for a one- two- or three-dimensional structure of the Bose-Einstein condensate

The phase transition from a classical atomic gas to a Bose-Einstein condensate takes place when a critical phase space density is reached, i.e. when the density of the particles with almost the same momentum is large enough. Can the condensation take place as atomic or molecular chains (one-dimensional) or as surfaces (two-dimensional)?

Please indicate whether your answer is based on theoretical considerations or on observations.

Physics Asked by HolgerFiedler on December 28, 2020

The answer depends on the assumptions. E.g. a standard textbook result is that a (non-interacting) BEC is not possible in a one-dimensional ?harmonic potential. However, this is no longer true if you allow "power law traps", see Bagnato & Kleppner. In addition, Ketterle & van Druten showed that the transition temperature in 3D is lowered, if we consider a sample of a finite size instead of the thermodynamic limit. It was also proven, that lowering the dimension increases the transition temperature and is therefore favorable for BEC. Hence, you should really be careful on what assumptions you like operate.

Correct answer by Semoi on December 28, 2020

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