Abstract
In this lecture, we discuss a first method for linking small-body physics and the macroscopic properties of a fluid. This method, which goes by the name of " virial development ", can be used for slightly degenerate fluids. It consists in developing a thermodynamic function of the fluid, such as its pressure, in powers of density or fugacity. This type of development was proposed by Kamerlingh Onnes at the beginning of the 20th century for a fluid described by classical thermodynamics. Remarkably, the coefficient of the nth-order term (with n in practice of the order of 2 to 5) is calculable provided we know how to treat the n-body problem exactly, i.e. a " small " system, far from the macroscopic case.
We begin with a reminder of the basics of the thermodynamic description of a perfect quantum gas, described by Bose or Fermi statistics. We thus find a first source of deviation of the coefficients of the virial development with respect to a Boltzmann gas. In the second part, we focus on the first non-trivial virial coefficient. We detail its calculation in the case of " standard " interactions, of the van der Waals type, and we recover a famous result of Beth and Uhlenbeck. Finally, we discuss the case of resonant binary interactions, in particular the Fermi gas model of unitary spin 1/2. This is a system that is currently playing a central role in quantum gas physics, as it enables us to test different theoretical approaches by confronting them with experimental results.
