Is Bose-Einstein Condensation Possible in Two Dimensions?

[Clau]

Is it possible to have Bose-Einstein condensation in two dimensions? Why?

 

[Gokul43201]

According to the Mermin-Wagner theorem, not under equilibrium conditions.

 

[xepma]

Well, in the case of a non-interacting (ideal) Bosonic gas in a 2 dimensional harmonic oscillator you can determine quite easily at which temperature you would have a macroscopic occupation of the ground state. And indeed, this happens for T>0. So, well, this can be viewed as a B.E.C. For the occupation of the ground state you get something like:

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

Where $$N_0$$ is the number of the particles in the ground state, and N the total number of particles.


Don't know what this Mermin-Wagner theorem says about it. To be honest, never even heared of that theorem :)