2005/07/19 by Elliott H. Lieb, Robert Seiringer, Lieb, Elliott H. +3
Mathematics · Physics and Astronomy · #FOS: Physical sciences #Mathematical Physics (math-ph) #Statistical Mechanics (cond-mat.stat-mech) #cond-mat.stat-mech #math-ph #math.MP
paper · pdf · doi:10.48550/arxiv.math-ph/0507049
Contribution to the proceedings of the 2005 International Conference on Differential Equations and Mathematical Physics, University of Alabama, Birmingham
arxiv created 2005/07/19 · arxiv updated 2009/12/01
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 1/2 fermions, this is E ∼ E0 + (ℏ2/2m) 2 πN ρa, where E0 is the energy of the non-interacting system and ρ is the density.