Airyaveraged gradient corrections for twodimensional fermion gases
Abstract
Building on the discussion in Trappe et al. (2016), we present a systematic derivation of gradient corrections to the kineticenergy functional and the oneparticle density, in particular for twodimensional systems. We derive the leading gradient corrections from a semiclassical expansion based on Wigner's phase space formalism and demonstrate that the semiclassical kineticenergy density functional at zero temperature cannot be evaluated unambiguously. In contrast, a densitypotential functional description that effectively incorporates interactions provides unambiguous gradient corrections. Employing an averaging procedure that involves Airy functions, thereby partially resumming higherorder gradient corrections, we facilitate a smooth transition of the particle density into the classically forbidden region of arbitrary smooth potentials. We find excellent agreement of the semiclassical Airyaveraged particle densities with the exact densities for very low but finite temperatures, illustrated for a Fermi gas with harmonic potential energy. We furthermore provide criteria for the applicability of the semiclassical expansions at low temperatures. Finally, we derive a wellbehaved groundstate kineticenergy functional, which improves on the ThomasFermi approximation.
 Publication:

Annals of Physics
 Pub Date:
 October 2017
 DOI:
 10.1016/j.aop.2017.07.020
 arXiv:
 arXiv:1612.04048
 Bibcode:
 2017AnPhy.385..136T
 Keywords:

 Orbitalfree densityfunctional theory;
 Gradient corrections;
 Semiclassical expansions;
 Singleparticle density;
 Kinetic energy functional;
 Fermion gases;
 Condensed Matter  Quantum Gases;
 Physics  Atomic Physics;
 Quantum Physics
 EPrint:
 24 pages, 8 figures. Changes to version 1: layout modified, footnotes 1 &