Thomas-Fermi von Weizs\"acker theory for a harmonically trapped, two-dimensional, spin-polarized dipolar Fermi gas

TL;DR

This paper develops a density functional approach using Thomas-Fermi von Weizs"acker theory to describe the equilibrium properties of a two-dimensional, spin-polarized dipolar Fermi gas in a harmonic trap, emphasizing the kinetic and interaction energy functionals.

Contribution

It introduces a carefully constructed 2D kinetic energy functional and a local interaction energy functional for dipolar interactions, along with an efficient numerical method for equilibrium density calculation.

Findings

Validated the functional approach for various dipole strengths

Provided physical insights into the local representation of dipolar interactions

Developed a computationally efficient self-consistent density determination method

Abstract

We systematically develop a density functional description for the equilibrium properties of a two-dimensional, harmonically trapped, spin-polarized dipolar Fermi gas based on the Thomas-Fermi von Weizs\"acker approximation. We pay particular attention to the construction of the two-dimensional kinetic energy functional, where corrections beyond the local density approximation must be motivated with care. We also present an intuitive derivation of the interaction energy functional associated with the dipolar interactions, and provide physical insight into why it can be represented as a local functional. Finally, a simple, and highly efficient self-consistent numerical procedure is developed to determine the equilibrium density of the system for a range of dipole interaction strengths.