Groundstate energy of the lowdensity Fermi gas
Abstract
Recent developments in the physics of lowdensity trapped gases make it worthwhile to verify old, wellknown results that, while plausible, were based on perturbation theory and assumptions about pseudopotentials. We use and extend recently developed techniques to give a rigorous derivation of the asymptotic formula for the groundstate energy of a dilute gas of N fermions interacting with a shortrange, positive potential of scattering length a . For spin 1/2 fermions, this is ẼE^{0}+(ℏ^{2}/2m)2πNϱa , where E^{0} is the energy of the noninteracting system and ϱ is the density. A similar formula holds in two dimensions (2D), with ϱa replaced by ϱ/∣ln(ϱa^{2})∣ . Obviously this 2D energy is not the expectation value of a densityindependent pseudopotential.
 Publication:

Physical Review A
 Pub Date:
 May 2005
 DOI:
 10.1103/PhysRevA.71.053605
 arXiv:
 arXiv:mathph/0412080
 Bibcode:
 2005PhRvA..71e3605L
 Keywords:

 03.75.Ss;
 05.30.Fk;
 Degenerate Fermi gases;
 Fermion systems and electron gas;
 Mathematical Physics;
 Statistical Mechanics
 EPrint:
 LaTeX, 22 pages