The Chemical Potential for Interacting Fermions in a Harmonic Potential

Hui Liu, Yong Li, Yulian Wang +1 more

Philip Phillips, Ernest R. Davidson

Abstract The chemical potential μ, as it appears in density functional theory, is examined extensively for harmonically interacting spin‐½ fermions in three dimensions. For this system the energy and chemical potential are discontinuous functions of the particle number if the most straightforward equation is used to define the energy for a noninteger particle number.

L. F. Lemmens, F. Brosens, J. T. Devreese

F. Brosens, J. T. Devreese, L. F. Lemmens

The thermodynamical properties are calculated for a three-dimensional model of $N$ harmonically interacting spin-polarized fermions in a parabolic potential well. The obtained dependences of the chemical potential and of the internal energy on the complete range of the temperature and of the number of particles turn out to obey a scaling law, similar to the scaling from the continuum approximation for the density of states. The calculation technique is based on our path integral approach of symmetrized density matrices for identical particles in a parabolic confining well.

J. Cugnon, O. Harouna

F. Brosens, J. T. Devreese, L. F. Lemmens

The thermodynamical properties are calculated for a three-dimensional model of $N$ harmonically interacting spin-polarized fermions in a parabolic potential well. The obtained dependences of the chemical potential and of the internal energy on the complete range of the temperature and of the number of particles turn out to obey a scaling law, similar to the scaling from the continuum approximation for the density of states. The calculational technique is based on our path-integral approach of symmetrized density matrices for identical particles in a parabolic confining well.