Shell structure in the density profiles for noninteracting fermions in anisotropic harmonic confinement

TL;DR

This paper introduces a Green's function approach to accurately compute density profiles of noninteracting fermions in anisotropic harmonic traps, revealing quantum shell effects especially in highly anisotropic configurations.

Contribution

It presents a novel Green's function method for exact density profile calculations in anisotropic traps, extending analysis beyond spherical symmetry.

Findings

Shell effects are negligible in spherical traps with many particles.

Quantum effects are prominent in highly anisotropic traps even for mesoscopic particle numbers.

Deviations from Thomas-Fermi approximation are observable in anisotropic configurations.

Abstract

We develop a Green's function method to evaluate the exact equilibrium particle-density profiles of noninteracting Fermi gases in external harmonic confinement in any spatial dimension and for arbitrary trap anisotropy. While in a spherically symmetric configuration the shell effects are negligible in the case of large number of particles, we find that for very anisotropic traps the quantum effects due to single-level occupancy and the deviations from the Thomas-Fermi approximation are visible also for mesoscopic clouds.