Temperature dependence of density profiles for a cloud of non-interacting fermions moving inside a harmonic trap in one dimension

TL;DR

This paper extends a Green's function method to finite temperatures to analyze how thermal effects influence the density profiles of non-interacting fermions in a one-dimensional harmonic trap, highlighting the smoothing of quantum structures.

Contribution

It introduces a finite-temperature extension of an existing Green's function approach for calculating density profiles in 1D fermionic systems under harmonic confinement.

Findings

Thermal excitations smooth out quantum shell structures.

Particle spill-out increases due to thermal effects.

Density profiles approach semiclassical predictions at higher temperatures.

Abstract

We extend to finite temperature a Green's function method that was previously proposed to evaluate ground-state properties of mesoscopic clouds of non-interacting fermions moving under harmonic confinement in one dimension. By calculations of the particle and kinetic energy density profiles we illustrate the role of thermal excitations in smoothing out the quantum shell structure of the cloud and in spreading the particle spill-out from quantum tunnel at the edges. We also discuss the approach of the exact density profiles to the predictions of a semiclassical model often used in the theory of confined atomic gases at finite temperature.