Temperature dependence of density profiles for a cloud of   non-interacting fermions moving inside a harmonic trap in one dimension
  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. 
Z. Akdeniz (1,2), P. Vignolo (1), A. Minguzzi (1) and M. P. Tosi (1)   ((1) SNS-Pisa, (2) Univeristy of Istanbul)