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Chinese Physics Letters

Spin-1/2 Fermion Gas in One-Dimensional Harmonic Trap with Attractive Delta Function Interaction

Yahui Wang, Zhong-Qi Ma

Published Feb 1, 2017• 0 citations
Publisher

Abstract

In terms of the Thomas–Fermi method, we solve the ground state energy of the N-body 1D harmonically trapped spin-1/2 fermion gas with the attractive δ-function interaction in the limit N → ∞ .
DOI
10.1088/0256-307x/34/2/020501

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We derive the density functional for the ground-state energy of a two-dimensional, spin-polarized gas of neutral fermionic atoms with magnetic-dipole interaction, in the Thomas-Fermi-Dirac approximation. For many atoms in a harmonic trap, we give analytical solutions for the single-particle spatial density and the ground-state energy, in dependence on the interaction strength, and we discuss the weak-interaction limit that is relevant for experiments. We then lift the restriction of full spin polarization and account for a time-independent inhomogeneous external magnetic field. The field strength necessary to ensure full spin polarization is derived.