Quantum coherence

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Over what range is the Pauli Exclusion Principle important? As a chemist I take it as an atom, but that seems an arbitrary stipulation. For instance, in metals how far apart must 2 electrons be to have the same 4 quantum numbers? I have seen that it has to do more with quantum coherence field than a certain space range. What determines the extent of the quantum coherence?

John Thompson
 
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Vanadium 50
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Over what range is the Pauli Exclusion Principle important?
Forever. You always have to antisymmetrize the wavefunction. Whether or not that makes a noticeable difference to anything you observe depends on how much you can notice.
 
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Pauli exclusion is important in any matter that has radiated down to its ground state (such that there aren't many more transitions left to happen, if any.) These systems include:
  • Blocks of metal, whose electrons occupy something fairly close to one giant pile of degeneracy.
  • Atoms, like you mentioned.
  • White dwarfs.
In all of these cases, the system has lost enough energy that it is not predominately the motion of the material that keeps it from collapsing. (A gas, I think, would be mainly held up by motion and not by quantum effects; PV=nRT comes from the mechanics of the atoms bouncing around.)

All fermions will end up in situations where exclusion is important if you cool them down enough. If you heat them up enough, they fly up in to the high states and populate them so sparsely that exclusion stops being important. Examples of those things would be turning metal in to plasma, ionizing electrons away from atoms, and going from white dwarfs to living stars which are kept very hot by fusion.
 
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