Recently a path integral method was developed in the research group for Theoretical Solid State Physics at the UIA to describe analytically a system of identical particles in a parabolic confining well, subject to a harmonic interparticle interaction or a magnetic field . Within the framework of the path integral formalism, an expression for the generating function of the partition function was derived, which enables to calculate the canonical partition function recursively for a system with quadratic two body interactions, even in the presence of a magnetic field . This is a starting-point for the exact treatment of thermodynamical properties, such as the internal energy, the heat capacity, and correlation functions, e.g., density, pair correlation function.
The goal of the present project is to examine the effect of an interaction between particles with spin degrees of freedom within this theory, which was developed both for bosons and fermions. We investigate the formation of coherent states and pairs, and the effects resulting from the finite amount of particles. This study provides a model that will serve as a trial system to examine more realistic systems like quantum dots, mesoscopic structures and superconducting clusters by perturbative and variational methods.