Physical review. B, Condensed matter

Two-dimensional virial and spin-wave coefficients of spin-polarized gases (H↑, D↑, He3 )

Valérie Lefèvre-Seguin, Henri Guignes, C. Lhuillier

Published Jul 1, 1987• 20 citations

Abstract

We present a quantum phase-shift calculation of the two-dimensional second virial coefficient ${B}_{2}^{2\mathrm{D}}$ and spin-wave characteristic parameters for spin-polarized quantum gases H\ensuremath{\uparrow}, D\ensuremath{\uparrow}, and $^{3}\mathrm{He}$. Emphasis is put on the study of quantum exchange effects which become essential in the 1-K range and below. The dependence of ${B}_{2}^{2\mathrm{D}}$ upon the nuclear polarization is analyzed. The calculation of statistics-independent coefficients is extended up to 50 K. The effect of a reduced dimensionality on the second virial and spin-wave coefficients is discussed and demonstrated by a comparison between 2D and 3D results. Two-dimensional bound states of helium dimers are estimated with the best present potential of Aziz et al. to be ${E}_{B}$${(}^{3}$He${\mathrm{\ensuremath{-}}}^{3}$He; 2D)=-0.88\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}5}$ K and ${E}_{B}$${(}^{3}$He${\mathrm{\ensuremath{-}}}^{4}$He; 2D)=-3.38 mK.

DOI: 10.1103/physrevb.36.141

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Virial calculations for H↓ in two and three dimensions

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Jan 1, 19830 citations

Physical review. B, Condensed matter

Two-dimensional virial and spin-wave coefficients of spin-polarized gases (H↑, D↑, He3 )

Valérie Lefèvre-Seguin, Henri Guignes, C. Lhuillier

Published Jul 1, 1987• 20 citations

Publisher

Abstract

We present a quantum phase-shift calculation of the two-dimensional second virial coefficient

{B}_{2}^{2\mathrm{D}}

and spin-wave characteristic parameters for spin-polarized quantum gases H\ensuremath{\uparrow}, D\ensuremath{\uparrow}, and

^{3}\mathrm{He}

. Emphasis is put on the study of quantum exchange effects which become essential in the 1-K range and below. The dependence of

{B}_{2}^{2\mathrm{D}}

upon the nuclear polarization is analyzed. The calculation of statistics-independent coefficients is extended up to 50 K. The effect of a reduced dimensionality on the second virial and spin-wave coefficients is discussed and demonstrated by a comparison between 2D and 3D results. Two-dimensional bound states of helium dimers are estimated with the best present potential of Aziz et al. to be

{E}_{B}$${(}^{3}

{\mathrm{\ensuremath{-}}}^{3}

He; 2D)=-0.88\ifmmode\times\else\texttimes\fi{}

{10}^{\mathrm{\ensuremath{-}}5}

K and

{E}_{B}$${(}^{3}

{\mathrm{\ensuremath{-}}}^{4}

He; 2D)=-3.38 mK.

DOI: 10.1103/physrevb.36.141

Related papers

Virial calculations for H↓ in two and three dimensions

E. V. L. de Mello, John J. Rehr, O. E. Vilches

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Spin polarized hydrogen and helium are being studied extensively because they are expected to exhibit quantum effects on a macroscopic scale. Here, low density properties of spin polarized hydrogen gas in two and three dimensions are studied using a quantum virial expansion. These properties include heat capacities, chemical potentials, and estimates of critical temperatures and densities for Bose-Einstein condensation in three dimensions and for a possible superfluid transition in two dimensions. The classical virial expansion and the validity of effective-range theory is also discussed. The heat capacity of adsorbed helium films of 3He, 4He and spin polarized 3He is also studied. Virial calculations with a structureless substrate approximation but with substrate mediated corrections to the Lennard-Jones potential are performed as a function of applied magnetic field and magnetization. Effects of substrate potential and geometry on the thermodynamics, low density submonolayer helium films physisorbed on rare gas plated graphite substrates are investigated using a tight-binding formalism and a lattice version of potential scattering theory. A generalization of the formalism to lattices with a basis is made and applied to the honeycomb lattice. The calculations with this theory exhibit systematic trends in the specific heat that are in qualitative agreement with presentlymore » available experimental data.« lessSpin polarized hydrogen and helium are being studied extensively because they are expected to exhibit quantum effects on a macroscopic scale. Here, low density properties of spin polarized hydrogen gas in two and three dimensions are studied using a quantum virial expansion. These properties include heat capacities, chemical potentials, and estimates of critical temperatures and densities for Bose-Einstein condensation in three dimensions and for a possible superfluid transition in two dimensions. The classical virial expansion and the validity of effective-range theory is also discussed. The heat capacity of adsorbed helium films of 3He, 4He and spin polarized 3He is also studied. Virial calculations with a structureless substrate approximation but with substrate mediated corrections to the Lennard-Jones potential are performed as a function of applied magnetic field and magnetization. Effects of substrate potential and geometry on the thermodynamics, low density submonolayer helium films physisorbed on rare gas plated graphite substrates are investigated using a tight-binding formalism and a lattice version of potential scattering theory. A generalization of the formalism to lattices with a basis is made and applied to the honeycomb lattice. The calculations with this theory exhibit systematic trends in the specific heat that are in qualitative agreement with presentlymore » available experimental data.« less

Jan 1, 19830 citations

We present a quantum phase-shift calculation of the two-dimensional second virial coefficient

{B}_{2}^{2\mathrm{D}}

and spin-wave characteristic parameters for spin-polarized quantum gases H\ensuremath{\uparrow}, D\ensuremath{\uparrow}, and

^{3}\mathrm{He}

. Emphasis is put on the study of quantum exchange effects which become essential in the 1-K range and below. The dependence of

{B}_{2}^{2\mathrm{D}}

{E}_{B}$${(}^{3}

{\mathrm{\ensuremath{-}}}^{3}

He; 2D)=-0.88\ifmmode\times\else\texttimes\fi{}

{10}^{\mathrm{\ensuremath{-}}5}

K and

{E}_{B}$${(}^{3}

{\mathrm{\ensuremath{-}}}^{4}

He; 2D)=-3.38 mK.

Using a second-order quantum virial expansion, we theoretically study the high-temperature thermodynamics of spin-polarized Fermi gases with

p

-wave interaction confined in two-dimensional harmonic traps. The second virial coefficient is calculated based on the energy spectrum of two harmonically trapped fermions. We find that the two-body spectrum can correctly be evaluated only when the

p

-wave effective range is properly considered, which is referred to as the well-known Wigner's bound. According to the quantum virial expansion, the high-temperature thermodynamics of the system is then discussed based on the two-body solutions. In addition, we investigate the high-temperature behavior of

p

-wave contacts in harmonic traps within the quantum virial expansion, which characterize a set of universal relations of strongly interacting spin-polarized Fermi gases. Our results can provide an accurate benchmark at high temperature for future numerical simulations as well as high-precision thermodynamic measurements of harmonically trapped spin-polarized Fermi gases in two dimensions.