Correlation in Momentum Space of Tonks-Girardeau Gas

TL;DR

This paper studies the momentum space correlations of the ground state of Tonks-Girardeau gases using Fourier transforms of coordinate space wavefunctions, revealing localized correlation features and natural orbital properties.

Contribution

It provides an exact analysis of momentum space correlations in Tonks-Girardeau gases using Bose-Fermi mapping and Fourier transformation techniques.

Findings

Correlations are significant only in small momentum regions.

The momentum space pair correlation vanishes in most regions.

Lowest natural orbital and occupation distribution are characterized.

Abstract

We investigate the correlation properties of the ground state of Tonks-Gigrardeal gases in the momentum space. With Bose-Fermi mapping method the exact ground state wavefunction in coordinate space can be obtained basing on the wavefunction of spin-polarized Fermions. By Fourier transformation we obtain the ground state wavefunction in momentum space, and therefore the momentum distribution, pair correlation and the reduced one-body density matrix (ROBDM) in momentum space. The ROBDM in momentum space is the Fourier transformation of the ROBDM in coordinate space and the pair correlation in momentun space is the Fourier transformation of the reduced two-body density matrix in coordinate space. The correlations in momentum space display larger values only in small momentum region and vanish in most other regions. The lowest natural orbital and occupation distribution are also obtained.