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In many assumptions, including those in drift velocity of electrons causing electric current, electrons are assumed to be moving just as molecules in gas phase. Can we just apply same analogy backwards?

Just as after certain critical temperature, electrons do not collide as there is exactly no resistance below critical temperature (where famous superconductivity occurs) Is there any temperature below which no collision in gas molecules take place?

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  • $\begingroup$ There is superfluidity. In liquid helium. $\endgroup$ – Pieter Jul 25 '17 at 9:12
  • $\begingroup$ Not really. While you can produce things like superfluid helium, that are in many ways analogous to a superconductor, it is not really reasonable to think of the material as a gas at that point. For that matter a better way to think about the critical temperature in a superconductor is that at $T_c$ a phase transition occurs and thinking about the electrons as a gas no longer really works. $\endgroup$ – By Symmetry Jul 25 '17 at 9:43
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There is indeed a strong analogy between a superconductor and a superfluid, and in some sense we can say that superconductivity is the superfluidity of the Fermi gas.

In a superconductor below the critical temperature, electrons form Cooper pairs that behave like bosons and condensate to the same ground state, just like the (bosonic) atoms of $^4$He during at the superfluid transition. Indeed, Cooper pairing is the mechanism responsible for the superfluidity of $^3$He, whose atoms are fermionic.

However, a classical models based on collisions is absolutely inadequate to explain the property of both a superconductor and a superfluid, and a quantum mechanical treatment is necessary.

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