Thermodynamics of Coupled Identical Oscillators within the Path Integral Formalism

TL;DR

This paper develops a path integral formalism to analyze the thermodynamics of coupled identical oscillators, including effects of interactions and magnetic fields, with a focus on bosonic condensation.

Contribution

It introduces a generalized symmetrized density matrix approach combined with generating functions to calculate partition functions for interacting identical particles.

Findings

Derived partition functions for particles with harmonic interactions

Analyzed effects of magnetic fields on thermodynamic properties

Provided insights into bosonic condensation phenomena

Abstract

A generalization of symmetrized density matrices in combination with the technique of generating functions allows to calculate the partition function of identical particles in a parabolic confining well. Harmonic two-body interactions (repulsive or attractive) are taken into account. Also the influence of a homogeneous magnetic field, introducing anisotropy in the model, is examined. Although the theory is developed for fermions and bosons, special attention is payed to the thermodynamic properties of bosons and their condensation.