F. Brosens et al., THERMODYNAMICS OF COUPLED IDENTICAL OSCILLATORS WITHIN THE PATH-INTEGRAL FORMALISM, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics, 55(1), 1997, pp. 227-236
A generalization of symmetrized density matrices in combination with t
he technique of generating functions allows one to calculate the parti
tion function of identical particles in a parabolic confining well. Ha
rmonic two-body interactions (repulsive or attractive) are taken into
account. Also the influence of a homogeneous magnetic field, introduci
ng anisotropy in the model, is examined. Although the theory is develo
ped for fermions and bosons, special attention is paid to the thermody
namic properties of bosons and their condensation.