Fuzzy and cool melodies

Abstract

In the previous chapter, we anticipated that the grand canonical description is naturally fit to describe systems where quantum effect become dominant. We move therefore to the quantum world, where we are going to discover the surprising melodies played by an orchestra of “fuzzy” players, those identical and indistinguishable particles that, in the Maxwell–Boltzmann limit, did not show their truly odd nature. In this journey, the grand canonical distribution will play the same role as Virgil in guiding Dante along his visit to the afterlife. Considering the warning at the entrance of the latter (Abandon all hope, you who enter here), and since I am surely not as well–versed in physics as Dante was in poetry, we better take a rather short trip, but long enough to discover some astonishing effects of purely quantum origin. In particular, we shall see that particle indistinguishability generates macroscopic correlation effects that are totally unexpected on classical grounds. We are indeed going to discover that the mysteries of quantum mechanics are not confined to the microscopic world, but rather emerge on length scales that we are accustomed to consider as fully classical.