Testing the nonlocal kinetic energy functional of an inhomogeneous, two-dimensional degenerate Fermi gas within the average density approximation

Abstract

In a recent paper [Phys. Rev. A 89, 022503 (2014)], the average density approximation (ADA) was implemented to develop a parameter-free, nonlocal kinetic energy functional to be used in the orbital-free density-functional theory of an inhomogenous, two-dimensional (2D), Fermi gas. In this work, we provide a detailed comparison of self-consistent calculations within the ADA with the exact results of the Kohn-Sham density-functional theory, and the elementary Thomas-Fermi (TF) approximation. We demonstrate that the ADA for the 2D kinetic energy functional works very well under a wide variety of confinement potentials, even for relatively small particle numbers. Remarkably, the TF approximation for the kinetic energy functional, without any gradient corrections, also yields good agreement with the exact kinetic energy for all confining potentials considered, although at the expense of the spatial and kinetic energy densities exhibiting poor point-wise agreement, particularly near the TF radius. Our findings illustrate that the ADA kinetic energy functional yields accurate results for both the local and global equilibrium properties of an inhomogeneous 2D Fermi gas, without the need for any fitting parameters.

Leading gradient correction to the kinetic energy for two-dimensional fermion gases

“…Introduction Recent advances in the experimental creation and control of ultracold Fermi gases [1] in twodimensional (2D) geometries [2][3][4][5][6][7] have triggered theoretical work on the semiclassical description of fermionic atoms by density functional theory (DFT) [8][9][10][11]. While the Thomas-Fermi (TF) approximation to the kinetic-energy functional is accurate enough at the early stage of these investigations, better approximations will eventually be required for, say, more precise thermometry [12][13][14] and more realistic descriptions of interfaces in multi-component Fermi gases [15][16][17][18][19][20][21].…”

“…We are thus confronted with a dilemma: On the one hand, we know that the TF approximation cannot be exact; on the other hand, there is no established pathway toward nonzero corrections. It is understandable, then, that various ad-hoc corrections have been invented, such as the vW-type term [9] and the nonlocal average-density functional recently proposed by van Zyl et al [10,11].…”