The properties of Tonk-Girardeau Gas at Finite Temperature and Comparison with Polarized Free Fermions

TL;DR

This paper studies the finite-temperature properties of the Tonks-Girardeau gas in a harmonic trap, comparing its behavior with polarized free fermions across different temperature regimes using thermal Bose-Fermi mapping.

Contribution

It provides a detailed analysis of the thermodynamic properties of the Tonks-Girardeau gas and its comparison with polarized free fermions, highlighting differences at low temperature and similarities at high temperature.

Findings

Pair and density distributions match polarized free fermions at all temperatures.

Reduced one-body density matrix and momentum distribution show Bose properties at low temperature.

At high temperature, Tonks-Girardeau gas becomes indistinguishable from polarized free fermions.

Abstract

In the present paper we investigate the Tonks-Girardeau gas confined in a harmonic trap at finite temperature with thermal Bose-Fermi mapping method. The pair distribution, density distribution, reduced one-body density matrix, the occupations number of natural orbitals, and momentum distribution are evaluated. In the whole temperature regime the pair distribution and density distribution exhibit the same properties as those of polarized free Fermions because both of them depend on the modulus of wavefunction rather than wavefunction. While the reduced one-body density matrix, the natural orbital occupation, momentum distribution, which depend on wavefunction, of Tonks gas displays Bose properties different from polarized free Fermions at low temperature. At high temperature we can not distinguish Tonks gas from the polarized free Fermi gas by all properties qualitatively.