Momentum Distribution for Bosons with Positive Scattering Length in a Trap

TL;DR

This paper calculates the coordinate-momentum distribution of bosons with positive scattering length in a trap using local density approximation, comparing it with Wigner distribution for clarity, valid to first order in scattering length.

Contribution

It introduces a first-order calculation of the bosonic distribution in a trap and compares it with Wigner distribution to clarify its physical meaning.

Findings

Distribution calculated within local density approximation

Comparison with Wigner distribution for interpretation

Valid to first order in scattering length

Abstract

The coordinate-momentum double distribution function $\rho ({\bf r}, {\bf p}) d^{3}rd^{3}p$ is calculated in the local density approximation for bosons with positive scattering length $a$ in a trap. The calculation is valid to the first order of $a$. To clarify the meaning of the result, it is compared for a special case with the double distribution function $\rho_{w}d^{3} rd^{3}p$ of Wigner.