Ground state energy of the dilute spin-polarized Fermi gas: Upper bound via cluster expansion

Abstract

We prove an upper bound on the ground state energy of the dilute spin-polarized Fermi gas capturing the leading correction to the kinetic energy resulting from repulsive interactions. One of the main ingredients in the proof is a rigorous implementation of the fermionic cluster expansion of Gaudin, Gillespie and Ripka (Nucl. Phys. A, 176.2 (1971), pp. 237-260).

80 pages, 9 figures. v2: added discussion of ${\rho }^{10/3}$-term and fixed minor errors

References in corpus (4)

• The Second Order Upper Bound for the Ground Energy of a Bose Gas
• Abstract cluster expansion with applications to statistical mechanical systems
• Quantum Monte Carlo study of the role of p-wave interactions in ultracold repulsive Fermi gases
• On the growth of Lebesgue constants for convex polyhedra

Cited by in corpus (3)

• Almost optimal upper bound for the ground state energy of a dilute Fermi gas via cluster expansion
• Pressure of a dilute spin-polarized Fermi gas: Lower bound
• The Huang-Yang formula for the low-density Fermi gas: upper bound