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

TL;DR

This paper establishes an upper bound on the ground state energy of a dilute spin-polarized Fermi gas, incorporating interaction effects through a rigorous fermionic cluster expansion.

Contribution

It introduces a rigorous implementation of the fermionic cluster expansion to derive energy bounds for the system.

Findings

Derived an upper bound on the ground state energy

Captured the leading correction due to repulsive interactions

Validated the cluster expansion approach for fermionic systems

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).