# Bose Condensate

## Main Question or Discussion Point

Is this the right place to discuss Bose Einstein condensate.

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Is this the right place to discuss Bose Einstein condensate.
well here goes any way, i know that bosons can be made to condensate and whole atoms (as long as they have an even number of electrons) but what i would like to discuss is, can electrons (or positrons) condensate or is there some law that does not allow this. Either way could someone set me on the right track.
regards Scupy.

Hootenanny
Staff Emeritus
Gold Member
well here goes any way, i know that bosons can be made to condensate and whole atoms (as long as they have an even number of electrons) but what i would like to discuss is, can electrons (or positrons) condensate or is there some law that does not allow this. Either way could someone set me on the right track.
regards Scupy.
Boson's are particles with integer spin (photons, W Bosons, Phonons etc.) and obey Bose-Einstein statistics, which allows Boson's to form BECs.

However, electrons (and positrons, quarks, muons etc.) have half integer spin, are called Fermions and obey Fermi-Dirac statistics (as opposed to Bose-Einstein statistics). Fermions must also obey Pauli's exclusion principle which states that the overall wavefunction for two identical fermions must be anti-symmetric. Roughly speaking, this means that no two fermions can occupy the same quantum state at the same time. In other words, no two fermions can occupy the same point in space at the same time and therefore cannot form BECs.

Cthugha
However, fermionic condensates do exist and are still a highly researched topic.
Of course fermions can't form a condensate directly, but under certain circumstances one can force them to build bound pairs. The following two-particle statistics obey Bose-Einstein-statistics as the pairs are now composite bosons and can in some situations form a condensate. This mechanism is rather similar (although not the same) to the cooper pair mechanism of electrons in conventional superconductors.

Boson's are particles with integer spin (photons, W Bosons, Phonons etc.) and obey Bose-Einstein statistics, which allows Boson's to form BECs.

However, electrons (and positrons, quarks, muons etc.) have half integer spin, are called Fermions and obey Fermi-Dirac statistics (as opposed to Bose-Einstein statistics). Fermions must also obey Pauli's exclusion principle which states that the overall wavefunction for two identical fermions must be anti-symmetric. Roughly speaking, this means that no two fermions can occupy the same quantum state at the same time. In other words, no two fermions can occupy the same point in space at the same time and therefore cannot form BECs.
Thx Hootenanny, i need to check out the Fermi-Dirac stuff i think, this was not mentioned in the book i've been reading, Super-conductivity and super-fluidity.

However, fermionic condensates do exist and are still a highly researched topic.
Of course fermions can't form a condensate directly, but under certain circumstances one can force them to build bound pairs. The following two-particle statistics obey Bose-Einstein-statistics as the pairs are now composite bosons and can in some situations form a condensate. This mechanism is rather similar (although not the same) to the cooper pair mechanism of electrons in conventional superconductors.
Also thx Cthugha, do you know where i could find any information on Fermionic condensates, i would like to know the particulars, especially positron BEC's if they exist.

Cooper pairs in BCS theory of low-temperature superconductivity are the prototypical examples of fermions forming pairs and condensing.