# What kind of bosons can have Bose-Einstein Condensation?

I notice that some bosons can exhibit Bose-Einstein condensation while others cannot (photons, phonons). Is it true that the bosons can have BEC only when the total number of particles is conserved? In this case, the chemical potential approaches zero at $$T_c$$, and particles begin to cluster (significantly) in the ground state.

Btw, is the total number of phonons conserved in a system? If it is not, for photons and phonons, $$\mu=0$$ as particles are not conserved. Thus, no BEC?

What distinguishes between photons and some other bosons such that the total number of particles can be conserved or not?

#### DrDu

Well, for phonons that depends also somewhat on definition. Consider as an example some ferroelectric material like Sr Ti O_3. At elevated temperatures, the Ti atom sits on the mean in the center of an octahedron defined by the oxygen atoms. At lower temperatures the system changes from cubic symmetry to some lower symmetry and the Ti atoms are on the mean not in the center of gravity of the oxygen atoms. You may describe the situation in two different ways: In the first description, you quantize the motion always around the corresponding equilibrium position. It is clear that at lower and lower temperatures the number of phonons decreases and there is no BEC.
In the second point of view you always quantize the motion around the center of the octahedron. Then, the expectation value of the phonon field phi does not vanish in the ground state of low symmetry, <0|phi|0> neq 0, and you could describe this as a BEC of the phonons.

You may describe the situation in two different ways: In the first description, you quantize the motion always around the corresponding equilibrium position. It is clear that at lower and lower temperatures the number of phonons decreases and there is no BEC.
In the second point of view you always quantize the motion around the center of the octahedron. Then, the expectation value of the phonon field phi does not vanish in the ground state of low symmetry, <0|phi|0> neq 0, and you could describe this as a BEC of the phonons.
So it means whether there is phonon BEC depends on how you quantize the system? But does it have any physical implications whether there is BEC or not? Is the ambiguity a particular trait of phonons (quasiparticles)? Rubidium atoms have BEC regardless of how you describe it right?

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