Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:physics/0101030 · Chinese Physics Letters

Density Functional Theory Studies of Magnetically Confined Fermi Gas

Chen Yu-Jun, Ma Hong-Ru

Published Dec 13, 2000• 1 citation
arXivHTMLPDF

Abstract

A theory is developed for magnetically confined Fermi gas at a low temperature based on the density functional theory. The theory is illustrated by the numerical calculation of the density distributions of Fermi atoms 40 K with parameters according to DeMarco and Jin's experiment [Science, 285(1999)1703]. Our results are in close agreement with the experiment. To check the theory, we also performed calculations using our theory at a high temperature, which compared very well to the results of the classical limit. PACS: 31. 35. Ew, 05. 30. Fk, 51. 30. +i

DOI
10.1088/0256-307x/18/1/312

Related papers

Density profile of the weakly interacting Fermi gas confined in a potential well: Nonzero temperature

J. Oliva

A theory is developed for the low-temperature density profile of a weakly interacting normal Fermi gas confined within an arbitrary potential well. This problem is of interest in connection with magnetically confined spin-aligned atomic deuterium (${\mathrm{D}}_{\mathrm{\ensuremath{\downarrow}}}$). The approach used is based on the statement of constancy of the chemical potential in equilibrium. This involves the internal chemical potential, a functional of the density, which we treat within the local-density approximation. We develop an accurate approximate form for the local internal chemical potential: For a given low temperature, it is taken equal to the known forms at low density (classical) and higher density (quantum); for intermediate density we use an appropriate interpolant which smoothly connects the low- and high-density forms. Finite-temperature density profiles are evaluated for the ideal Fermi gas for parameters appropriate to magnetically confined ${\mathrm{D}}_{\mathrm{\ensuremath{\downarrow}}}$ for both symmetric linear and quadratic one-dimensionally varying wells. We also evaluate density profiles including the leading-order interparticle interaction effect. For conditions relevant to hypothetical ${\mathrm{D}}_{\mathrm{\ensuremath{\downarrow}}}$ at moderate densities this effect is found to be small but measurable.

Physical review. B, Condensed matter•Mar 1, 1989•11 citations

A new Fermi liquid: the normal phase of a strongly interacting gas of cold atoms

Sylvain Nascimbène, Nir Navon, Sebastiano Pilati +4 more

We measure the magnetic susceptibility of a Fermi gas with tunable interactions in the low-temperature limit and compare it to quantum Monte Carlo calculations. Experiment and theory are in excellent agreement and fully compatible with the Landau theory of Fermi liquids. We show that these measure- ments shed new light on the nature of the excitations of the normal phase of a strongly interacting Fermi gas.

•Dec 21, 2010•1 citation

Fermi-Liquid Behavior of the Normal Phase of a Strongly Interacting Gas of Cold Atoms

Sylvain Nascimbène, Nir Navon, Sebastiano Pilati +4 more

We measure the magnetic susceptibility of a Fermi gas with tunable interactions in the low-temperature limit and compare it to quantum Monte Carlo calculations. Experiment and theory are in excellent agreement and fully compatible with the Landau theory of Fermi liquids. We show that these measurements shed new light on the nature of the excitations of the normal phase of a strongly interacting Fermi gas.

arXiv:1012.4664•Physical Review Letters•May 27, 2011•105 citations

Very Low-Temperature Fermi Gas

Franz Mohling

The momentum distribution in a low-temperature Fermi gas is investigated using the methods of quantum statistics developed by Lee and Yang together with the linked-pair expansions of the previous paper. It is shown that in order to determine the momentum distribution at very low temperatures two coupled integral equations must be considered, one in momentum variables and due to Lee and Yang, and the other in temperature variables. It is also shown that the dominant low-temperature behavior of the momentum distribution can be extracted in terms of a certain function ${\ensuremath{\nu}}^{\ensuremath{'}}(\mathrm{k})$. For a low-density Fermi gas with strong, short-range, two-body interactions, it is shown to third order in the scattering parameters of the interaction that at $T=0$ the function ${\ensuremath{\nu}}^{\ensuremath{'}}(\mathrm{k})$ is equal to the free particle momentum distribution. Also, the energy and other thermodynamic quantities are expressed in terms of ${\ensuremath{\nu}}^{\ensuremath{'}}(\mathrm{k})$, so that the theory permits a generalization of perturbation theoretic results to nonzero temperatures. The ground-state energy, momentum distribution, and thermodynamic potential are calculated to third order in the scattering parameters.

Physical Review•May 15, 1961•35 citations

Universal thermodynamics of a strongly interacting Fermi gas: theory versus experiment

Hui Hu, Xia-Ji Liu, P. D. Drummond

Strongly interacting, dilute Fermi gases exhibit a scale-invariant, universal thermodynamic behavior. This is notoriously difficult to understand theoretically because of the absence of a small interaction parameter. Here, we present a systematic comparison of theoretical predictions from different quantum many-body theories with recent experimental data of Nascimbne et al (2010 Nature 463 1057). Our comparisons have no adjustable parameters, either theoretically or experimentally. All the model approximations seem to fluctuate rather than converge on the experimental data. It turns out that a simple Gaussian pair fluctuation theory gives the best quantitative agreement, except at the critical superfluid transition region. In the normal state, we also calculate the equation of state by using a quantum cluster expansion theory and explore in detail its applicability to low temperatures. Using the accurate experimental result for the thermodynamic function S ( T ), we determine the temperature T of a trapped Fermi gas at unitarity as a function of a non-interacting temperature T i , which can be obtained by an adiabatic sweep to the free gas limit. By analyzing the recent experimental data, we find a characteristic temperature ( T / T F ) 0 =0.19±0.02 or ( T i / T F ) 0 =0.16±0.02 in a harmonic trap, below which there are deviations from normal Fermi-liquid-like behavior that may be attributed to pairing effects. Here, T F is the Fermi temperature for a trapped ideal, non-interacting Fermi gas. Our thorough comparison may shed light on the further theoretical development of strongly interacting fermions.

arXiv:1001.2085•New Journal of Physics•Jun 30, 2010•72 citations

Kinetic Description of Rotating Gases in External Magnetic Fields in the Framework of the Thomas-Fermi-Dirac Approach

Vincenzo G. Molinari, Federico Rocchi, M. Sumini

Aim of this work is to extend the results obtained in a previous study on the magnetic confinement and stability of a rotating quantum degenerate fermion gas. This extension consists in the inclusion in the previously set up model of the effects of the exchange forces, and generalises the Thomas-Fermi (TF) approach used in the referenced work towards a Thomas-Fermi-Dirac (TFD) statistical description. The TF model has not only been used extensively and with success in these years to study atomic, nuclear, and molecular properties, or to evaluate features of matter in extreme conditions such as low temperatures and/or high densities typical of astrophysics and inertial confinement fusion experiments, but also to found hydrodynamic theories for the diffusion and stability of fermion plasmas (Rozsnyai, B. F. ([1972] Rozsnyai, B. F. 1972. Relativistic Hartree-Fock-Slater calculations for arbitrary temperature and matter density. Phys. Rev. A, 5(3): 1137–1149. [Crossref] , [Google Scholar]). Relativistic Hartree-Fock-Slater calculations for arbitrary temperature and matter density. Phys. Rev. A 5(3):1137–1149), one component nonneutral degenerate fluids, plasmas etc. In this article an equation for density profiles in cylindrical symmetry is found, from the semiclassical kinetic theory of quantum gases (Pathria, R. K. ([1996] Pathria, R. K. 1996. Statistical Mechanics. , 2nd ed. Oxford: Butterworth & Heinemann. [Google Scholar]). Statistical Mechanics. 2nd ed. Oxford: Butterworth & Heinemann), which takes into account the effects of temperature, average velocity, external magnetic field and quantum exchange. Numerical and approximate analytical solutions of this equation for the case of complete quantum degeneracy are given and comparisons with the previous results are carried out.

Transport Theory and Statistical Physics•Jan 11, 2003•1 citation
A theory is developed for magnetically confined Fermi gas at a low temperature based on the density functional theory. The theory is illustrated by the numerical calculation of the density distributions of Fermi atoms 40 K with parameters according to DeMarco and Jin's experiment [Science, 285(1999)1703]. Our results are in close agreement with the experiment. To check the theory, we also performed calculations using our theory at a high temperature, which compared very well to the results of the classical limit. PACS: 31. 35. Ew, 05. 30. Fk, 51. 30. +i
A theory is developed for the low-temperature density profile of a weakly interacting normal Fermi gas confined within an arbitrary potential well. This problem is of interest in connection with magnetically confined spin-aligned atomic deuterium (${\mathrm{D}}_{\mathrm{\ensuremath{\downarrow}}}$). The approach used is based on the statement of constancy of the chemical potential in equilibrium. This involves the internal chemical potential, a functional of the density, which we treat within the local-density approximation. We develop an accurate approximate form for the local internal chemical potential: For a given low temperature, it is taken equal to the known forms at low density (classical) and higher density (quantum); for intermediate density we use an appropriate interpolant which smoothly connects the low- and high-density forms. Finite-temperature density profiles are evaluated for the ideal Fermi gas for parameters appropriate to magnetically confined ${\mathrm{D}}_{\mathrm{\ensuremath{\downarrow}}}$ for both symmetric linear and quadratic one-dimensionally varying wells. We also evaluate density profiles including the leading-order interparticle interaction effect. For conditions relevant to hypothetical ${\mathrm{D}}_{\mathrm{\ensuremath{\downarrow}}}$ at moderate densities this effect is found to be small but measurable.
The momentum distribution in a low-temperature Fermi gas is investigated using the methods of quantum statistics developed by Lee and Yang together with the linked-pair expansions of the previous paper. It is shown that in order to determine the momentum distribution at very low temperatures two coupled integral equations must be considered, one in momentum variables and due to Lee and Yang, and the other in temperature variables. It is also shown that the dominant low-temperature behavior of the momentum distribution can be extracted in terms of a certain function ${\ensuremath{\nu}}^{\ensuremath{'}}(\mathrm{k})$. For a low-density Fermi gas with strong, short-range, two-body interactions, it is shown to third order in the scattering parameters of the interaction that at T=0T=0T=0 the function ${\ensuremath{\nu}}^{\ensuremath{'}}(\mathrm{k})$ is equal to the free particle momentum distribution. Also, the energy and other thermodynamic quantities are expressed in terms of ${\ensuremath{\nu}}^{\ensuremath{'}}(\mathrm{k})$, so that the theory permits a generalization of perturbation theoretic results to nonzero temperatures. The ground-state energy, momentum distribution, and thermodynamic potential are calculated to third order in the scattering parameters.
Strongly interacting, dilute Fermi gases exhibit a scale-invariant, universal thermodynamic behavior. This is notoriously difficult to understand theoretically because of the absence of a small interaction parameter. Here, we present a systematic comparison of theoretical predictions from different quantum many-body theories with recent experimental data of Nascimbne et al (2010 Nature 463 1057). Our comparisons have no adjustable parameters, either theoretically or experimentally. All the model approximations seem to fluctuate rather than converge on the experimental data. It turns out that a simple Gaussian pair fluctuation theory gives the best quantitative agreement, except at the critical superfluid transition region. In the normal state, we also calculate the equation of state by using a quantum cluster expansion theory and explore in detail its applicability to low temperatures. Using the accurate experimental result for the thermodynamic function S ( T ), we determine the temperature T of a trapped Fermi gas at unitarity as a function of a non-interacting temperature T i , which can be obtained by an adiabatic sweep to the free gas limit. By analyzing the recent experimental data, we find a characteristic temperature ( T / T F ) 0 =0.19±0.02 or ( T i / T F ) 0 =0.16±0.02 in a harmonic trap, below which there are deviations from normal Fermi-liquid-like behavior that may be attributed to pairing effects. Here, T F is the Fermi temperature for a trapped ideal, non-interacting Fermi gas. Our thorough comparison may shed light on the further theoretical development of strongly interacting fermions.
Aim of this work is to extend the results obtained in a previous study on the magnetic confinement and stability of a rotating quantum degenerate fermion gas. This extension consists in the inclusion in the previously set up model of the effects of the exchange forces, and generalises the Thomas-Fermi (TF) approach used in the referenced work towards a Thomas-Fermi-Dirac (TFD) statistical description. The TF model has not only been used extensively and with success in these years to study atomic, nuclear, and molecular properties, or to evaluate features of matter in extreme conditions such as low temperatures and/or high densities typical of astrophysics and inertial confinement fusion experiments, but also to found hydrodynamic theories for the diffusion and stability of fermion plasmas (Rozsnyai, B. F. ([1972] Rozsnyai, B. F. 1972. Relativistic Hartree-Fock-Slater calculations for arbitrary temperature and matter density. Phys. Rev. A, 5(3): 1137–1149. [Crossref] , [Google Scholar]). Relativistic Hartree-Fock-Slater calculations for arbitrary temperature and matter density. Phys. Rev. A 5(3):1137–1149), one component nonneutral degenerate fluids, plasmas etc. In this article an equation for density profiles in cylindrical symmetry is found, from the semiclassical kinetic theory of quantum gases (Pathria, R. K. ([1996] Pathria, R. K. 1996. Statistical Mechanics. , 2nd ed. Oxford: Butterworth & Heinemann. [Google Scholar]). Statistical Mechanics. 2nd ed. Oxford: Butterworth & Heinemann), which takes into account the effects of temperature, average velocity, external magnetic field and quantum exchange. Numerical and approximate analytical solutions of this equation for the case of complete quantum degeneracy are given and comparisons with the previous results are carried out.