Virial expansion coefficients in the harmonic approximation

TL;DR

This paper calculates virial expansion coefficients for an interacting fermionic system using a harmonic approximation, providing insights into thermodynamic behavior across temperature regimes.

Contribution

It introduces a method to compute virial coefficients for many-fermion systems within a harmonic approximation, bridging low and high temperature limits.

Findings

Virial coefficients depend on dimension, temperature, and interaction.

Interpolation reproduces ground state and high-temperature limits.

Results show shell effects are smoothed with increasing temperature.

Abstract

The virial expansion method is applied within a harmonic approximation to an interacting N-body system of identical fermions. We compute the canonical partition functions for two and three particles to get the two lowest orders in the expansion. The energy spectrum is carefully interpolated to reproduce ground state properties at low temperature and the non-interacting large temperature limit of constant virial coefficients. This resembles the smearing of shell effects in finite systems with increasing temperature. Numerical results are discussed for the second and third virial coefficients as function of dimension, temperature, interaction, and the transition temperature between low and high energy limits.