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APS

Weizsacker energy of unitary Fermi gas in a harmonic trap

Alexander L. Zubarev

Published May 1, 2009• 0 citations
OpenAlex

Abstract

The universal method of construction of the rigorous lower bounds to the Weizsäcker energy is presented. We study a few-fermion system at the unitarity. Upper and lower bounds to the density functional theory (DFT) ground state energy within the local density approximation (LDA) are given. The rigorous lower bounds to the accuracy of the method are derived. PACS numbers: 31.15.Ew, 71.15.Mb, 03.75.Ss

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Weizsacker energy of unitary Fermi gas in a harmonic trap

Alexander L. Zubarev

The universal method of construction of the rigorous lower bounds to the Weizsacker energy is presented. We study a few-fermion systemat the unitarity. Upper and lower bounds to the density functional theory(DFT) ground state energy within the local density approximation (LDA) aregiven. Therigorous lower bounds to the accuracy of the method are derived.

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Chang and Bertsch [Phys. Rev. A 76, 021603(R) (2007)] proposed a simple formula for the ground state energy of a unitary Fermi gas in a harmonic trap, based on their Green's function Monte Carlo simulations of up to 22 fermions, combined with general assumptions about the universal thermodynamic behavior of the unitary Fermi gas. In this work, we perform the ab initio simulations of the ground state energy of up to one hundred fermions using the fictitious identical particle method to overcome the Fermion sign problem, and we find that the formula proposed by Chang and Bertsch remains highly accurate. Since the number of fermions we simulate is much larger than that simulated by Chang and Bertsch when they proposed the formula, our work provides strong evidence for the universal validity of the formula. Our work demonstrates that fictitious identical particles provide a valuable tool for the ab initio simulations of ultracold Fermi gases.

arXiv:2403.02961•Mar 5, 2024•0 citations
The universal method of construction of the rigorous lower bounds to the Weizsäcker energy is presented. We study a few-fermion system at the unitarity. Upper and lower bounds to the density functional theory (DFT) ground state energy within the local density approximation (LDA) are given. The rigorous lower bounds to the accuracy of the method are derived. PACS numbers: 31.15.Ew, 71.15.Mb, 03.75.Ss
We have considered the orbital-free approximation of the kinetic energy functional to investigate the zero temperature properties of dilute harmonically trapped two component Fermi gas at unitarity. It is shown that our approach provides a realible and inexpensive method to study superfluid strongly interacting dilute Fermi gases. PACS numbers: 31.15.Ew, 71.15.Mb, 03.75.SsThe modern density functional theory (DFT) is based on the Kohn-Sham (KS) approach [1], where the noninteracting kinetic energy, T, is calculated in terms of the KS orbitals, although Ref.[2] proved the basic existence of functional T(ρ), where ρ is the density, ρ(⃗r)d
Chang and Bertsch [Phys. Rev. A 76, 021603(R) (2007)] proposed a simple formula for the ground state energy of a unitary Fermi gas in a harmonic trap, based on their Green's function Monte Carlo simulations of up to 22 fermions, combined with general assumptions about the universal thermodynamic behavior of the unitary Fermi gas. In this work, we perform the ab initio simulations of the ground state energy of up to one hundred fermions using the fictitious identical particle method to overcome the Fermion sign problem, and we find that the formula proposed by Chang and Bertsch remains highly accurate. Since the number of fermions we simulate is much larger than that simulated by Chang and Bertsch when they proposed the formula, our work provides strong evidence for the universal validity of the formula. Our work demonstrates that fictitious identical particles provide a valuable tool for the ab initio simulations of ultracold Fermi gases.