Multi or single quantum state?

[fxdung]

Is Bose condensation state a multiparticle state or many single identical states?
Can we apply Pauli principle to two electrons that one is on the Earth and the other is on the Moon?

 

[vanhees71]

It's a many-body state. The point is that an arbitrary number of bosons can occupy the ground state. At temperature $0$ for a gas of particles whose number is conserved, all these particles are in the ground state. So you can have a Bose Einstein condensate with an arbitrary number of bosons.

 

[fxdung]

Why can we conceptually refer to the many-body state but not many single body at many identical ground states?The conceptual difference leads to difference conclusions e.g about the resistance of superconductor is zero(nearly) or not.
And what about the 2ed question on Pauli principle on Fermions?

 

[vanhees71]

I don't understand the first question about the many-boson state. The $N$-boson states can be written as superpositions of totally symmetriced tensor products of $N$ single-particle states. One possibility is that all $N$ boson states occupy the same single-particle state, i.e., it's the $N$-fold tensor product of this one single-particle state. For the BEC this single-particle state is the one-particle ground state.

As to the Pauli principle on fermions. There you have the totally antisymmetrized tensor products of single-particle states as a basis, and of course two electrons localized at far distances have to be antisymmetrized. Any two electrons in the universe are antisymmetrized two-particle states or superpositions of those (or statistical operators living in this fermionic many-body Hilbert space), but for far-distant experiments this doesn't play a big role as long as you do only local experiments, i.e., you do cannot observe possible correlations due to a possible entanglement of far-distant electrons except you do coincidence experiments on the two far distant places on the entangled electron pairs ("linked-cluster theorem").

 

[fxdung]

In superconductor the Cooper pairs are condensated to the state having minimum free energy.All they have the same quantum numbers,then we can explain the zero R as follow: the collision of phonon with electron is neglected because it interact with the whole number of electrons that all in a same state.But we can not explain as such that if each electron lies in an identical single particle state.Each collision will pull each electron out of the state separatelly, so R is different to zero.
Is the tensor representation suitable for non-interacting particles?

 

[fxdung]

Now,I can understand that can be explained by the coherence in phase of the identical single states.

 

[fxdung]

Because of coherence in phases of the identical single states,the BEC state of many Boson particles is macrostate ( macro wave function).Then any friction of impurity lattice in superconductor acts on whole electrons that in the superconductivity phase.All Boson particles in BEC state can be considered as a ''bulk''.The phases of single states sum up to the phase of BEC state,but this state is in classical limit,the phase of BEC state is classical action of the system.Then the whole number of the Boson particles can be considered as an entity.Is that correct?

 

[fxdung]

Now I think in BEC state all Bose particles have ''equal right''and we can not dishtinguish idendentical particles,all the particles having same phases(same states),so in the multiparticle state all they can be considered as a whole in interaction with other particles.Is that correct?