Statistical mechanics of a system of interacting bosons

Abstract

The equilibrium properties of a system of interacting bosons are studied by the methods of quantum field theory. The problem is formulated in terms of a density matrix in an irreducible representation so as to be able to treat the degenerate as well as the nondegenerate phase. The quantities of basic interest are considered to be the one-particle, time-dependent Green's functions of the system from which the free energy can be obtained through suitable prescriptions. Explicit expressions are derived for the various thermodynamic functions in the weak-interaction approximation for the self-energy parts. To the first order in the interaction v 0, the behaviour of the thermodynamic functions is such as would correspond to a second-order phase transition across the line of condensation. To the order (v 3 2 0) , the specific heat diverges proportional to ( n - n c ) -1 2 as the density n approaches the critical density n c from the degenerate phase. The inverse compressibility on the other hand becomes negative for densities sufficiently close to the critical density indicating that the weak interaction results, or the formally equivalent low density results, are valid in the neighbourhood of the transition line in an asymptotic sense only.