electron- electron attraction

[swansont]

 

What experiments say is that

- There is a condensation energy

- The quantum flux shows TWO electrons together, not 10²³

 

They don't say that ALL electrons are in the same state. Maybe they don't even tell that the paired electrons are of opposite spin, nor even in the same state except for spin: some reports tell that the paired electrons have opposite momentums, which then doesn't need paired spins.

 

 

But ONE ground state does mean no movement. Movement and acceleration need a change of state. And energy does not mean quantity of movement.

 

 

Cool down! BCS is known not to work for higher temperature superconductors. And what I see everywhere, be it on Wiki; Hyperphysics, or the ideas here gained there, is not BCS, with a very high probability. So defending things like "bosons all in the same state" is not necessarily defending BCS.

 

The condensation energy is a feature of a bose condensate and is part of the theory, which is really successful for the type of superconductors it describes. You can't get this with fermions — they must be composite bosons. Saying that there is a condensation and most of these electron pairs are in the ground state is saying the same thing.

 

In QM, the ground state of a potential does not mean there is no kinetic energy.

 

If you have a problem with this I suggest you go read up on QM, and on Bose condensates in general and specifically on BCS. Raising objections based on ignorance of the theory is a non-starter.

[Enthalpy]

Swansont, I appreciate you. On most occurences, I agree with you, even if I don't feel the need to tell it everytime. Sometimes I disagree, and that's normal life: no reason to loose one's good mood.

 

Electrons making pairs doesn't suffice to let them condensate to some ground state. Atoms prove it. Electrons are paired in atoms, making bosons, but these pairs do not condensate to the 1s orbital.

 

On the other hand, supercooled atoms form Bose-Einstein condensates.

 

The difference must reside in the density of the condensation candidate. Realized BEC use gas, where the atoms have much space between them. At enough distance, the bosonic atom behaves like one single boson, because the effects of its constituent fermions decrease quickly. So bosonic atoms can condensate, provided they have enough empty space between them - and provided one doesn't check for instance if two atoms are close enough to overlap their shells, which is a departure from the simple boson condensate picture.

 

As opposed, electrons in an atom are about as wide as the atom, and their mean distance as well, so each pair cannot react with an other pair as global bosons would. Pairs act as two fermions, and don't condensate to the same state which is as small as the pairs themselves.

 

Now, if I consider a metal or superconductor:

 

The electrons near the Fermi level are very delocalized, much broader than their mean distance (I don't consider the electrons clearly deeper than the Fermi level, since for them, "localized" and "distance" has no interesting meaning, because we can't attribute a weighed sum of states to one particular electron; the best to say is "all states are occupied"). Their interaction distance as well exceeds their mean geometric distance. Because these electrons near the Fermi level - and pairs if applicable - are so much bigger than the mean distance, they must be in the atom-like situation, where no condensation can take place.

 

The heat capacity at the superconducting transition is a strong argument against a Bose-Einstein condensate. This heat capacity confirms the law of a single energy gap. This is consistent with electrons pairing and nothing more, with approximately the same energy for each pair. It is not consistent with pairs condensing further once formed, which would leave more heat capacity than observed at temperatures below the superconducting transition.

 

The Bose-Einstein condensate in superconductivity was part of the London theory, superseded by BCS. The BEC can well have been added later in the presentations of BCS.

[swansont]

Electrons making pairs doesn't suffice to let them condensate to some ground state. Atoms prove it. Electrons are paired in atoms, making bosons, but these pairs do not condensate to the 1s orbital.

The electron "pairing" in atoms is not due to an external confining potential. It's a different kind of pairing.

 

 

On the other hand, supercooled atoms form Bose-Einstein condensates.

 

The difference must reside in the density of the condensation candidate. Realized BEC use gas, where the atoms have much space between them. At enough distance, the bosonic atom behaves like one single boson, because the effects of its constituent fermions decrease quickly. So bosonic atoms can condensate, provided they have enough empty space between them - and provided one doesn't check for instance if two atoms are close enough to overlap their shells, which is a departure from the simple boson condensate picture.

 

As opposed, electrons in an atom are about as wide as the atom, and their mean distance as well, so each pair cannot react with an other pair as global bosons would. Pairs act as two fermions, and don't condensate to the same state which is as small as the pairs themselves.

Nobody is claiming that electrons within an atom condense. This is moot.

 

Now, if I consider a metal or superconductor:

 

The electrons near the Fermi level are very delocalized, much broader than their mean distance (I don't consider the electrons clearly deeper than the Fermi level, since for them, "localized" and "distance" has no interesting meaning, because we can't attribute a weighed sum of states to one particular electron; the best to say is "all states are occupied"). Their interaction distance as well exceeds their mean geometric distance. Because these electrons near the Fermi level - and pairs if applicable - are so much bigger than the mean distance, they must be in the atom-like situation, where no condensation can take place.

 

The heat capacity at the superconducting transition is a strong argument against a Bose-Einstein condensate. This heat capacity confirms the law of a single energy gap. This is consistent with electrons pairing and nothing more, with approximately the same energy for each pair. It is not consistent with pairs condensing further once formed, which would leave more heat capacity than observed at temperatures below the superconducting transition.

 

The Bose-Einstein condensate in superconductivity was part of the London theory, superseded by BCS. The BEC can well have been added later in the presentations of BCS.

I have two options: believe you, or believe the physics community. The latter win by the sheer tonnage of backing evidence and agreement with theories that work in many other situations. You have a beef with BCS theory. Fine. How about you tell the Nobel prize-winners how wrong they are. This isn't the place for it.

[Enthalpy]

Exact, electron pairs don't condense in an atom, so pairs being bosons does not suffice in an atom, and may not suffice in a superconductor.

 

Pairing in an atom just permits two electrons, the maximum number, to occupy the most favourable available orbital, in response to the nucleus' confinement potential.

 

The evidence in favour of pairing in BCS, notably the heat capacity curve versus the temperature, speaks against a Bose-Einstein condensate.

 

I still don't know if the BEC, which I doubt takes place, was a part of BCS, which I have nothing against. I know that science relies on models working better or worse - and this is your third option in addition to believing -, not on the reputation of people (or rather: it shouldn't...), and it is my opinion that a science forum can as well.

[swansont]

Again: spin pairing in orbital filling is a completely separate phenomenon. There is no confining potential between the electrons, so there is no reason for them to form a composite boson. You are comparing apples and oranges.

[Phi for All]

I still don't know if the BEC, which I doubt takes place, was a part of BCS, which I have nothing against. I know that science relies on models working better or worse - and this is your third option in addition to believing -, not on the reputation of people (or rather: it shouldn't...), and it is my opinion that a science forum can as well.

!

Moderator Note

I know you'll be good for goodness' sake and start your own thread if you want to continue a discussion on the shortcomings of BCS theory. Stocking. Coal. Bad.

[Enthalpy]

You are a wise person, and I followed your advice there:

http://www.scienceforums.net/topic/80823-no-bose-einstein-condensate-in-bcs-superconductor-theory/