Can indistinguishable particles obey Boltzmann statistics

[DrClaude]

Are you beginning to see the problem? If C60 truly behaved like a boson you would be able to put any number of particles into the same state (or "point" in phase space). I find that really hard to imagine. I think they'll simply and very classically be in each others way, even considering the effects of uncertainty. To me it seems that quantum statistics simply doesn't apply to systems that are "too classical".

Bose-Einstein condensates of molecules exist. While no one has been able to cool molecule as big as C₆₀ down to temperatures where BEC happens, there is no reason to think it doesn't make sense for many C₆₀ molecules to be in the same quantum state.

By the way, double-slit type experiments have been performed using C₆₀ (and even bigger molecules), and quantum effects are visible.

 

[Philip Koeck]

Bose-Einstein condensates of molecules exist. While no one has been able to cool molecule as big as C₆₀ down to temperatures where BEC happens, there is no reason to think it doesn't make sense for many C₆₀ molecules to be in the same quantum state.

By the way, double-slit type experiments have been performed using C₆₀ (and even bigger molecules), and quantum effects are visible.

Thanks. Experiments are always convincing. Maybe it is time to skip all classical statistics and start directly with quantum statistics as vanHees suggested earlier.

 

[Philip Koeck]

One more thing has turned up. It's been mentioned several times (also on Wikipedia and in textbooks) that the Boltzmann distribution is a high temperature and low occupancy limiting case of the BE and FD distributions. I can show that W approaches the correct Boltzmann counting for low occupancy as discussed in posts 69 to 73 (before calculating a distribution), but I'm having a hard time seeing how high T would help in general. Only if I insert expressions for the chemical potential and density of states that are valid for an ideal gas of indistinguishable particles into the BE or FD distribution, I get something that approaches the Boltzmann distribution for high T. Is the mentioned limiting case general or only valid for the ideal gas? Can anyone point me to some literature?

 

[bhobba]

but I'm having a hard time seeing how high T would help in general.

See the following:
https://ps.uci.edu/~cyu/p115A/LectureNotes/Lecture13/lecture13.pdf

The distribution depends on a parameter β which is small at high temperatures. This gives the familiar Boltzmann-Maxwell distribution..

Thanks
Bill