arXiv:0909.0305 · Chinese Physics Letters

Ground State Energy for Fermions in a 1D Harmonic Trap with Delta Function Interaction

Zhong-Qi Ma, Chongming Yang

Published Dec 1, 2009• 10 citations

Abstract

Conjectures are made for the ground state energy of a large spin 1/2 Fermion system trapped in a 1D harmonic trap with delta function interaction. States with different spin J are separately studied. The Thomas–Fermi method is used as an effective test for the conjecture.

DOI: 10.1088/0256-307x/26/12/120505

Related papers

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

Yahui Wang, Zhong-Qi Ma

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 → ∞ .

Chinese Physics LettersFeb 1, 20170 citations

Two interacting fermions in a one-dimensional harmonic trap: Matching the Bethe ansatz and variational approaches

Diefferson Rubeni da Rosa de Lima, Angela Foerster, I. Roditi

In this work, combining the Bethe ansatz approach with the variational principle, we calculate the ground-state energy of the relative motion of a system of two fermions with spin up and spin down interacting via a delta-function potential in a one-dimensional (1D) harmonic trap. Our results show good agreement with the analytical solution of the problem, and provide a starting point for the investigation of more complex few-body systems where no exact theoretical solution is available.

arXiv:1208.2206Physical Review AOct 19, 201223 citations

Ground State of Fermions in a 1D Trap with δ Function Interaction

Chongming Yang

The ground state of fermions in a 1D trap with δ function interaction is studied mathematically with group theory ideas.

Chinese Physics LettersDec 1, 200923 citations

Unitary Fermi gas in a harmonic trap

S. Y. Chang, G. F. Bertsch

arXiv:physics/0703190Physical Review AAug 2, 200774 citations

Bosons or Fermions in 1D Power Potential Trap with Repulsive Delta Function Interaction

Zhong-Qi Ma, Chongming Yang

We study the ground state of a 1D many Boson or Fermion system with repulsive delta function interparticle interaction trapped in an external potential V(x) = |x| a /2 where a > 0.

Chinese Physics LettersSep 1, 20103 citations

Ground state energy of a dilute inhomogeneous Fermi gas

Thomas Gamet

arXiv:2510.21268Oct 24, 20250 citations

arXiv:0909.0305 · Chinese Physics Letters

Ground State Energy for Fermions in a 1D Harmonic Trap with Delta Function Interaction

Zhong-Qi Ma, Chongming Yang

Published Dec 1, 2009• 10 citations

arXiv HTML PDF

Abstract

DOI: 10.1088/0256-307x/26/12/120505

Related papers

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

Yahui Wang, Zhong-Qi Ma

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 → ∞ .

Chinese Physics LettersFeb 1, 20170 citations

Two interacting fermions in a one-dimensional harmonic trap: Matching the Bethe ansatz and variational approaches

Diefferson Rubeni da Rosa de Lima, Angela Foerster, I. Roditi

arXiv:1208.2206Physical Review AOct 19, 201223 citations

Ground State of Fermions in a 1D Trap with δ Function Interaction

Chongming Yang

The ground state of fermions in a 1D trap with δ function interaction is studied mathematically with group theory ideas.

Chinese Physics LettersDec 1, 200923 citations

Unitary Fermi gas in a harmonic trap

S. Y. Chang, G. F. Bertsch

We present an ab initio calculation of small numbers of trapped, strongly interacting fermions using the Green's function Monte Carlo method. The ground-state energy, density profile, and pairing gap are calculated for particle numbers $N=2--22$ using the parameter-free ``unitary'' interaction. Trial wave functions are taken in the form of correlated pairs in a harmonic oscillator basis. We find that the lowest energies are obtained with a minimum explicit pair correlation beyond that needed to exploit the degeneracy of oscillator states. We find that the energies can be well fitted by the expression ${a}_{\mathit{TF}}{E}_{\mathit{TF}}+\ensuremath{\Delta}\phantom{\rule{0.2em}{0ex}}\mathrm{mod}(N,2)$ where ${E}_{\mathit{TF}}$ is the Thomas-Fermi energy of a noninteracting gas in the trap and $\ensuremath{\Delta}$ is the pairing gap. There is no evidence of a shell correction energy in the systematics, but the density distributions show pronounced shell effects. We find the value $\ensuremath{\Delta}=0.7\ifmmode\pm\else\textpm\fi{}0.2\ensuremath{\omega}$ for the pairing gap. This is smaller than the value found for the uniform gas at a density corresponding to the central density of the trapped gas.We present an ab initio calculation of small numbers of trapped, strongly interacting fermions using the Green's function Monte Carlo method. The ground-state energy, density profile, and pairing gap are calculated for particle numbers $N=2--22$ using the parameter-free ``unitary'' interaction. Trial wave functions are taken in the form of correlated pairs in a harmonic oscillator basis. We find that the lowest energies are obtained with a minimum explicit pair correlation beyond that needed to exploit the degeneracy of oscillator states. We find that the energies can be well fitted by the expression ${a}_{\mathit{TF}}{E}_{\mathit{TF}}+\ensuremath{\Delta}\phantom{\rule{0.2em}{0ex}}\mathrm{mod}(N,2)$ where ${E}_{\mathit{TF}}$ is the Thomas-Fermi energy of a noninteracting gas in the trap and $\ensuremath{\Delta}$ is the pairing gap. There is no evidence of a shell correction energy in the systematics, but the density distributions show pronounced shell effects. We find the value $\ensuremath{\Delta}=0.7\ifmmode\pm\else\textpm\fi{}0.2\ensuremath{\omega}$ for the pairing gap. This is smaller than the value found for the uniform gas at a density corresponding to the central density of the trapped gas.

arXiv:physics/0703190Physical Review AAug 2, 200774 citations

Bosons or Fermions in 1D Power Potential Trap with Repulsive Delta Function Interaction

Zhong-Qi Ma, Chongming Yang

We study the ground state of a 1D many Boson or Fermion system with repulsive delta function interparticle interaction trapped in an external potential V(x) = |x| a /2 where a > 0.

Chinese Physics LettersSep 1, 20103 citations

Ground state energy of a dilute inhomogeneous Fermi gas

Thomas Gamet

We study the ground state energy of a system of N fermions with two spin states in the large N limit. The particles are placed in an inhomogeneous trapping potential and interact via scaled interactions. We study a dilute limit where the range of the interaction potential is much smaller than the typical inter-particle distance. We show that the energy per particle converges to the Thomas-Fermi energy of the system, with a perturbative term corresponding tot he interaction and exhibiting the scattering length of the potential. The proof is decomposed into two bounds. First, we construct an appropriate test-state to prove the upper bound. Then, we prove the lower bound by the Dyson lemma, which allows us to regularize the interaction potential, and several semi-classical tools.We study the ground state energy of a system of N fermions with two spin states in the large N limit. The particles are placed in an inhomogeneous trapping potential and interact via scaled interactions. We study a dilute limit where the range of the interaction potential is much smaller than the typical inter-particle distance. We show that the energy per particle converges to the Thomas-Fermi energy of the system, with a perturbative term corresponding tot he interaction and exhibiting the scattering length of the potential. The proof is decomposed into two bounds. First, we construct an appropriate test-state to prove the upper bound. Then, we prove the lower bound by the Dyson lemma, which allows us to regularize the interaction potential, and several semi-classical tools.

arXiv:2510.21268Oct 24, 20250 citations

N=2--22

using the parameter-free ``unitary'' interaction. Trial wave functions are taken in the form of correlated pairs in a harmonic oscillator basis. We find that the lowest energies are obtained with a minimum explicit pair correlation beyond that needed to exploit the degeneracy of oscillator states. We find that the energies can be well fitted by the expression ${a}_{\mathit{TF}}{E}_{\mathit{TF}}+\ensuremath{\Delta}\phantom{\rule{0.2em}{0ex}}\mathrm{mod}(N,2)$ where

{E}_{\mathit{TF}}

is the Thomas-Fermi energy of a noninteracting gas in the trap and $\ensuremath{\Delta}$ is the pairing gap. There is no evidence of a shell correction energy in the systematics, but the density distributions show pronounced shell effects. We find the value $\ensuremath{\Delta}=0.7\ifmmode\pm\else\textpm\fi{}0.2\ensuremath{\omega}$ for the pairing gap. This is smaller than the value found for the uniform gas at a density corresponding to the central density of the trapped gas.