Universal Energy Functionals for Trapped Fermi Gases in Low Dimensions

Jiansen Zhang; Shina Tan

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arXiv · 2312.00325

Universal Energy Functionals for Trapped Fermi Gases in Low Dimensions

Jiansen Zhang·Shina Tan

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Abstract

We study the system of trapped two-component Fermi gases with zero-range interaction in two dimensions (2D) or one dimension (1D). We calculate the one-particle density matrices of these systems at small displacements, from which we show that the $N$-body energies are linear functionals of the occupation probabilities of single-particle energy eigenstates. A universal energy functional was first derived in 2011 for trapped zero-range interacting two-component Fermi gases in three dimensions (3D). We also calculate the asymptotic behaviors of the occupation probabilities of single-particle energy eigenstates at high energies.

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Jiansen Zhang, Shina Tan. 2023-12-01. Universal Energy Functionals for Trapped Fermi Gases in Low Dimensions. https://arxiv.org/abs/2312.00325

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