On the Thomas-Fermi approximation for Bose condensates in traps

TL;DR

This paper revisits the Thomas-Fermi approximation for Bose condensates in traps, showing that the phase-space distribution aligns with classical predictions without large N assumptions, even for small particle numbers.

Contribution

It demonstrates that the Thomas-Fermi approximation accurately describes Bose condensates in traps across a range of particle numbers without relying on large N limits.

Findings

Phase-space distribution matches classical delta function form.

Kinetic energy agrees with quantum results for low and intermediate N.

Attractive interactions are also effectively described.

Abstract

Thomas-Fermi theory for Bose condesates in inhomogeneous traps is revisited. The phase-space distribution function in the Thomas-Fermi limit is $f_0(\bold{R},\bold{p})$ $\alpha$ $\delta(\mu - H_{cl})$ where $H_{cl}$ is the classical counterpart of the self-consistent Gross-Pitaevskii Hamiltonian. No assumption on the large N-limit is introduced and, e.g the kinetic energy is found to be in good agreement with the quantal results even for low and intermediate particle numbers N. The attractive case yields conclusive results as well.