From the path-integral to the thermodynamics of quantum solids

Starting from the path integral formulation of quantum statistical mechanics, an effective potential can be defined which allows us to reduce the evaluation of quantum equilibrium averages to classical configuration integrals. The method is after applied to two interesting models. The first one is the one dimensional lattice with exponential interactions, known as the Toda lattice; we choose it as an example to show how our method can be usefully employed to obtain information not only on macroscopic thermodynamic functions, but also on the dynamical response functions. The second system we consider is a 3D one, i.e. an fcc lattice of atoms interacting through a Lennard-Jones potential, which is a good model for rare gas solids, whose experimental thermodynamic properties in the all range of temperature come out to be well reproduced by our approach.