TY - JOUR

T1 - Ground-state energy of the low-density Fermi gas

AU - Lieb, Elliott H.

AU - Seiringer, Robert

AU - Solovej, Jan Philip

PY - 2005/5

Y1 - 2005/5

N2 - 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.

AB - 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.

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U2 - 10.1103/PhysRevA.71.053605

DO - 10.1103/PhysRevA.71.053605

M3 - Article

AN - SCOPUS:26944492677

SN - 1050-2947

VL - 71

JO - Physical Review A - Atomic, Molecular, and Optical Physics

JF - Physical Review A - Atomic, Molecular, and Optical Physics

IS - 5

M1 - 053605

ER -