Most Quantum Monte Carlo work on Fermionic systems deals with a number of particles on the order of 10^2. The numerical work suggest even such a small number ca

Most Quantum Monte Carlo work on Fermionic systems deals with a number of particles on the order of 10^2. The numerical work suggest even such a small number can superconduct and we have seen experimentally that there are superconducting nano-particles that can be very small indeed. I don’t recall off the top of my head how many atoms are in the smallest ones we’ve seen though. As far as pen-and-paper theoretical work goes though, something like 10^2 atoms is actually more difficult than 10^23 of them because 10^23 is basically infinite for our purposes so there are all sorts of useful limits one can take. When you consider something like 10^2 atoms, many useful approximations go out the window. You can no longer ignore the physics at the edge of the material since everything is very close to the edge, you can’t make assumptions about homogeneity, statistical arguments about the aggregate behaviour of electrons become unreliable, etc.