Eur. Phys. J. B 29, 105-115 (2002)
https://doi.org/10.1140/epjb/e2002-00267-9

The partition function of an interacting many body system

Beyond the perturbed static path approximation (PSPA)

¹ Physik-Department der Technischen Universität München, James-Franck-Strasse, 85747 Garching, Germany
² Fakultät für Physik, Albert-Ludwigs-Universität Freiburg, Hermann-Herder-Strasse 3, 79104 Freiburg, Germany

Corresponding author: ^a crummel@ph.tum.de

Received: 28 March 2002
Published online: 17 September 2002

Abstract

Based on the path integral approach the partition function of a many body system with separable two body interaction is calculated in the sense of a semiclassical approximation. The commonly used Gaussian type of approximation, known as the perturbed static path approximation (PSPA), breaks down near a crossover temperature due to instabilities of the classical mean field solution. It is shown how the PSPA is systematically improved within the crossover region by taking into account large non-Gaussian fluctuations and an approximation applicable down to very low temperatures is carried out. These findings are tested against exact results for the archetypical cases of a particle moving in a one dimensional double well and the exactly solvable Lipkin-Meshkov-Glick model. The extensions should have applications in finite systems at low temperatures as in nuclear physics and mesoscopic systems, e.g. for gap fluctuations in nanoscale superconducting devices previously studied within a PSPA type of approximation.