10.1103/PhysRevA.71.053605
Lieb, Élliott H
Élliott
Lieb
Robert Seiringer
Robert
Seiringer
Solovej, Jan P
Jan
Solovej
Ground state energy of the low density Fermi gas
American Physical Society
2005
2018-12-11T11:57:13Z
2019-04-26T07:22:11Z
journal_article
https://research-explorer.app.ist.ac.at/record/2362
https://research-explorer.app.ist.ac.at/record/2362.json
Recent developments in the physics of low-density trapped gases make it worthwhile to verify old, well-known 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 ground-state energy of a dilute gas of N fermions interacting with a short-range, positive potential of scattering length a. For spin-12 fermions, this is E∼E0+(22m)2πNa, where E0 is the energy of the noninteracting system and is the density. A similar formula holds in two dimensions (2D), with a replaced by ln(a2). Obviously this 2D energy is not the expectation value of a density-independent pseudopotential.