Composite Bosons: Understanding Their Behavior at Near Absolute Zero

[TrickyDicky]

Matter with even total spin are considered (composite) bosons, for instance atoms whose particle spins add up to an even number, but they don't behave at all like gauge bosons, and I don't think they follow Bose-Einstein statistics,unless they are cooled to near absolute zero temperature, in which case they show BEC features, but then also fermionic matter can be made to turn "bosonic" with sufficiently low temperatures (He-3 BEC,etc).
So my question is does the bosonic behaviour in composite bosons shows only in near absolute zero conditions,and if so, why call them bosons at all if fermions can be made to show that behaviour at extreme temperatures?

 

[ZapperZ]

Matter with even total spin are considered (composite) bosons, for instance atoms whose particle spins add up to an even number, but they don't behave at all like gauge bosons, and I don't think they follow Bose-Einstein statistics,unless they are cooled to near absolute zero temperature, in which case they show BEC features, but then also fermionic matter can be made to turn "bosonic" with sufficiently low temperatures (He-3 BEC,etc).
So my question is does the bosonic behaviour in composite bosons shows only in near absolute zero conditions,and if so, why call them bosons at all if fermions can be made to show that behaviour at extreme temperatures?

Er.. Cooper pairs in high-Tc superconductors are composite bosons as well. They show bosonic behavior at the critical temperatures, which can be as high as 130-150K.

Zz.

 

[Cthugha]

Two comments: Fermionic matter does not turn bosonic at low temperatures. You can get pairing or similar mechanisms such that the composite particle is a composite boson. And bosonic behavior for composite bosons is not limited to low temperatures. Excitons for example keep their bosonic nature up to room temperature in certain materials. It is more a matter of density. If the density of composite bosons becomes large, their fermionic components determining their inner structure cannot be neglected anymore.

 

[TrickyDicky]

Two comments: Fermionic matter does not turn bosonic at low temperatures. You can get pairing or similar mechanisms such that the composite particle is a composite boson. And bosonic behavior for composite bosons is not limited to low temperatures. Excitons for example keep their bosonic nature up to room temperature in certain materials. It is more a matter of density. If the density of composite bosons becomes large, their fermionic components determining their inner structure cannot be neglected anymore.

Thanks for trying to answer. What are excitons?
I guess what I meant to ask is what are the differenes between bosonic and fermionic matter at room tmperature. So your reference to density is very interesting, At what density would composite bosons show their bosonic nature and how?

 

[Cthugha]

Excitons are elementary excitations in semiconductors. Maybe you know that in semiconductors one kind of excitations consists of electrons promoted to the conduction band. Simply speaking, those leave quasiparticles called holes behind in the valence band. As both have opposite charge, it is possible that they form a bound electron hole pair somewhat similar to hydrogen. This composite pair of electron and hole is an exciton and it is approximately bosonic.

You can identify bosons in terms of commutation relations. For excitons, the commutation relation at low density is the same as for bosons, but it in principle it depends on density, ending up in the fermionic commutation relations of the fermionic constituents at high density when the Coulomb interaction of the constituents belonging to different excitons becomes comparable to the binding energy of the electron-hole pairs.

 

[TrickyDicky]

Excitons are elementary excitations in semiconductors. Maybe you know that in semiconductors one kind of excitations consists of electrons promoted to the conduction band. Simply speaking, those leave quasiparticles called holes behind in the valence band. As both have opposite charge, it is possible that they form a bound electron hole pair somewhat similar to hydrogen. This composite pair of electron and hole is an exciton and it is approximately bosonic.

You can identify bosons in terms of commutation relations. For excitons, the commutation relation at low density is the same as for bosons, but it in principle it depends on density, ending up in the fermionic commutation relations of the fermionic constituents at high density when the Coulomb interaction of the constituents belonging to different excitons becomes comparable to the binding energy of the electron-hole pairs.

What would be the low density limit in lay terms? can you point me to some text where this is treated in introductory form?
Thanks

 

[Cthugha]

What exactly can be defined as low density depends on the interactions that can happen between the composite bosons. If they are heavy and interact strongly, a smaller density is sufficient to show deviations from bosonic behavior than is needed for weakly interacting and light particles.

I do not really know any really intoductory texts. However, there are some review articles and some relatively easy to understand old articles.

One of the earlier treatments of this problem is given in M.D. Girardeau: "Second-quantization representation for a non relativistic system of composite particles, I Generalized Tani transformation and its iterative evaluation", J. Math. Phys. 16,1901 (1975).

A long and exhaustive (but not that easy to read) review article is found in A. Klein and E. R. Marshalek: "Boson realizations of Lie algebras with applications to nuclear physics", Rev. Mod. Phys. 63, 375–558 (1991).

To give the complete picture, there are also people, who claim that composite bosons are approximately bosonic, but the small deviations from true bosons without inner structure should always be considered. A review from this point of view is given for example in M. Combescot et al.: "The many-body physics of composite bosons", Physics Reports 463, 215–320 (2008).

I am sorry that these papers might be somewhat hard to digest, but I am not aware of texts which are easier to read.

 

[akhmeteli]

What would be the low density limit in lay terms? can you point me to some text where this is treated in introductory form?
Thanks

See my post https://www.physicsforums.com/showpost.php?p=1461845&postcount=5