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

Journal de physique

Transport properties in a spin polarized gas, III

C. Lhuillier

Published Jan 1, 1983• 124 citations
Publisher

Abstract

A complete quantum phase shift calculation of several transport coefficients in spin polarized quantum gases (3He, H↑ and D↑) has been carried out for temperatures ranging from 0.04 K to 10 K and nuclear polarizations M varying from 0 to 1. After a detailed analysis of the dynamical features of the collision, the various direct and exchange « cross sections » necessary to describe the collision between two spin-polarized atoms are studied Emphasis is then placed on some particle-indistinguishability consequences that could be seen in 3He or H↑ systems, such as the strong M dependence of the heat capacity, a mode coupling between heat capacity and longitudinal spin diffusion and the oscillatory character of the evolution of the transverse components of M.

DOI
10.1051/jphys:019830044010100

Related papers

Transport properties in a spin polarized gas, II

C. Lhuillier, Franck Laloë

The general results obtained in the preceding article are applied to the study of transport phenomena in a spin polarized gas at low temperatures, with particular emphasis on the particle indistinguishability effects in collisions. The effects of the nuclear orientation M are treated exactly (no M expansion). First, a simple theory of spin diffusion is presented and the response of the gas to a spin orientation gradient is calculated. The spin coherences and their evolution due to the « identical-spin rotation effect » are taken into account; it is found that they can play an important role, especially in the low temperature limit. The hydrodynamic equations of evolution of M are non-linear and anisotropic. Particle indistinguishability effects give an oscillatory character to the evolution of the transverse components of M (spin oscillations). Then, a more elaborate variational method is used to study the coupling between spin diffusion and heat conduction. This effect is, again, a sheer consequence of quantum interference phenomena introduced by particle indistinguishability. Finally, isotopic mixtures of 3He and 4He are considered In addition to coupling between isotopic diffusion and heat conduction, which exists for classical systems, quantum collision effects introduce a coupling between these two modes and spin diffusion.

Journal de physique•Jan 1, 1982•129 citations

Momentum and spin transport properties of spin polarized Fermi systems

Wei Lijuan

We carried out experiments on a spin polarized 3He- 4He mixture with 3He concentration x 3 = 6.26 × 10−4, and on pure 3He liquid. Spin polarization affects the transport properties of these Fermi systems. The effect on momentum transport was studied by using a vibrating-wire viscometer to measure viscosity of the 3He-4He mixture over the temperature range 6.09 mK–100 mK in 7.96 T and 1.00 T magnetic fields. A large viscosity increase was observed upon application of the 7.96 T magnetic field for temperature T < TF(TF = 19.5 mK is the Fermi temperature). The observed viscosity is in very good agreement with theoretical calculations for a dilute Fermi gas by Jeon and Mullin [1988, 1989] and Mullin and Jeon [1992]. The polarization effect on spin transport was investigated by measuring the transverse diffusion coefficient D ⊥ in pure 3He liquid at saturated vapor pressure and at 15.85 bar over the temperature range 4.5 mK–159 mK in a 7.96 T magnetic field. We used a pulsed NMR spin echo technique in a field gradient of 16.0 G/cm to do the measurements and fits to the Leggett equations [1970] to obtain D⊥. For T < 20 mK, we found D⊥ is less than measured in earlier experiments at lower magnetic fields. D⊥ does not increase with decreasing temperature as 1/T2, but appears to approach a constant as T → 0 while it is expected that the longitudinal spin diffusion coefficient D∥ ∝ 1/ T2. This is called spin diffusion anisotropy and it was observed for the first time in our 3He liquid experiments. The anisotropy temperature we determined for 3He liquid was Ta = 16.4 ± 2.2 mK at saturated vapor pressure and in a 7.96 T magnetic field. The transverse spin diffusion in 3 He results agree qualitatively with theories proposed by Meyerovich and Musaeflan [1992, 1994]. They also agree qualitatively with theories proposed by Golosov and Ruckenstein [1995, 1998] by extrapolation of the dilute theory to a strongly interacting system.

•Jan 1, 2001•0 citations

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

Valérie Lefèvre-Seguin, Henri Guignes, C. Lhuillier

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.

Physical review. B, Condensed matter•Jul 1, 1987•20 citations

Transverse spin diffusion in strongly interacting Fermi gases

Tilman Enss

We compute spin diffusion in a dilute Fermi gas at arbitrary temperature, polarization, and strong interaction in the normal phase using kinetic theory. While the longitudinal spin diffusivity ${D}_{\ensuremath{\parallel}}$ depends weakly on polarization and diverges for small temperatures, the transverse spin diffusivity ${D}_{\ensuremath{\perp}}$ has a strong polarization dependence and approaches a finite value for $T\ensuremath{\rightarrow}0$ in the Fermi liquid phase. For a 3D unitary Fermi gas at infinite scattering length, the diffusivities reach a minimum near the quantum limit of diffusion $\ensuremath{\hbar}/m$ in the quantum degenerate regime and are strongly suppressed by medium scattering, and we discuss the importance of the spin-rotation effect. In two dimensions, ${D}_{\ensuremath{\perp}}$ attains a minimum at strong coupling $\ensuremath{-}1\ensuremath{\lesssim}\mathrm{ln}({k}_{F}{a}_{2D})\ensuremath{\lesssim}1$ and reaches ${D}_{\ensuremath{\perp}}\ensuremath{\sim}0.2...\phantom{\rule{0.16em}{0ex}}0.3\phantom{\rule{0.16em}{0ex}}\ensuremath{\hbar}/m$ at large polarization. These values are consistent with recent measurements of two-dimensional ultracold atomic gases in the strong coupling regime.

arXiv:1307.5175•Physical Review A•Sep 27, 2013•19 citations

Thermodynamic properties of spin-polarized 3He gas in the temperature range 1 mK–4 K from the quantum second virial coefficient

Amal F. Al-Maaitah, Ayman S. Sandouqa, B.R. Joudeh +1 more

The quantum second virial coefficient B[Formula: see text] of 3He[Formula: see text] gas is determined in the temperature range 0.001–4 K from the Beth–Uhlenbeck formula. The corresponding phase shifts are calculated from the Lippmann–Schwinger equation using a highly-accurate matrix-inversion technique. A positive B[Formula: see text] corresponds to an overall repulsive interaction; whereas a negative B[Formula: see text] represents an overall attractive interaction. It is found that in the low-energy limit, B[Formula: see text] tends to increase with increasing spin polarization. The compressibility Z is evaluated as another measure of nonideality of the system. Z becomes most significant at low temperatures and increases with polarization. From the pressure–temperature (P–T) behavior of 3He[Formula: see text] at low T, it is deduced that P decreases with increasing T below 8 mK.

International Journal of Modern Physics B•Jun 8, 2017•4 citations

Spin rotation effects and spin waves in gaseous 3He↑

Pierre-Jean Nacher, Geneviève Tastevin, Michèle Leduc +2 more

Spin polarized gases such as H↑ or 3He↑ can propagate damped spin waves at low temperatures; their origin is the so-called « identical spin rotation effect » in collisions between identical particles. We report here the observation of such effects in 3He↑ in the temperature range 2 < T < 6 K, and preliminary measurements of the coefficient μ which characterizes the quality factor of the spin oscillations. The measurements are in agreement with the numerical calculations of C. Lhuillier.

Journal de Physique Lettres•Jan 1, 1984•71 citations
A complete quantum phase shift calculation of several transport coefficients in spin polarized quantum gases (3He, H↑ and D↑) has been carried out for temperatures ranging from 0.04 K to 10 K and nuclear polarizations M varying from 0 to 1. After a detailed analysis of the dynamical features of the collision, the various direct and exchange « cross sections » necessary to describe the collision between two spin-polarized atoms are studied Emphasis is then placed on some particle-indistinguishability consequences that could be seen in 3He or H↑ systems, such as the strong M dependence of the heat capacity, a mode coupling between heat capacity and longitudinal spin diffusion and the oscillatory character of the evolution of the transverse components of M.
The general results obtained in the preceding article are applied to the study of transport phenomena in a spin polarized gas at low temperatures, with particular emphasis on the particle indistinguishability effects in collisions. The effects of the nuclear orientation M are treated exactly (no M expansion). First, a simple theory of spin diffusion is presented and the response of the gas to a spin orientation gradient is calculated. The spin coherences and their evolution due to the « identical-spin rotation effect » are taken into account; it is found that they can play an important role, especially in the low temperature limit. The hydrodynamic equations of evolution of M are non-linear and anisotropic. Particle indistinguishability effects give an oscillatory character to the evolution of the transverse components of M (spin oscillations). Then, a more elaborate variational method is used to study the coupling between spin diffusion and heat conduction. This effect is, again, a sheer consequence of quantum interference phenomena introduced by particle indistinguishability. Finally, isotopic mixtures of 3He and 4He are considered In addition to coupling between isotopic diffusion and heat conduction, which exists for classical systems, quantum collision effects introduce a coupling between these two modes and spin diffusion.
We carried out experiments on a spin polarized 3He- 4He mixture with 3He concentration x 3 = 6.26 × 10−4, and on pure 3He liquid. Spin polarization affects the transport properties of these Fermi systems. The effect on momentum transport was studied by using a vibrating-wire viscometer to measure viscosity of the 3He-4He mixture over the temperature range 6.09 mK–100 mK in 7.96 T and 1.00 T magnetic fields. A large viscosity increase was observed upon application of the 7.96 T magnetic field for temperature T < TF(TF = 19.5 mK is the Fermi temperature). The observed viscosity is in very good agreement with theoretical calculations for a dilute Fermi gas by Jeon and Mullin [1988, 1989] and Mullin and Jeon [1992]. The polarization effect on spin transport was investigated by measuring the transverse diffusion coefficient D ⊥ in pure 3He liquid at saturated vapor pressure and at 15.85 bar over the temperature range 4.5 mK–159 mK in a 7.96 T magnetic field. We used a pulsed NMR spin echo technique in a field gradient of 16.0 G/cm to do the measurements and fits to the Leggett equations [1970] to obtain D⊥. For T < 20 mK, we found D⊥ is less than measured in earlier experiments at lower magnetic fields. D⊥ does not increase with decreasing temperature as 1/T2, but appears to approach a constant as T → 0 while it is expected that the longitudinal spin diffusion coefficient D∥ ∝ 1/ T2. This is called spin diffusion anisotropy and it was observed for the first time in our 3He liquid experiments. The anisotropy temperature we determined for 3He liquid was Ta = 16.4 ± 2.2 mK at saturated vapor pressure and in a 7.96 T magnetic field. The transverse spin diffusion in 3 He results agree qualitatively with theories proposed by Meyerovich and Musaeflan [1992, 1994]. They also agree qualitatively with theories proposed by Golosov and Ruckenstein [1995, 1998] by extrapolation of the dilute theory to a strongly interacting system.
We present a quantum phase-shift calculation of the two-dimensional second virial coefficient B22D{B}_{2}^{2\mathrm{D}}B22D​ and spin-wave characteristic parameters for spin-polarized quantum gases H\ensuremath{\uparrow}, D\ensuremath{\uparrow}, and 3He^{3}\mathrm{He}3He. Emphasis is put on the study of quantum exchange effects which become essential in the 1-K range and below. The dependence of B22D{B}_{2}^{2\mathrm{D}}B22D​ 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 EB{E}_{B}EB​(3{(}^{3}(3He${\mathrm{\ensuremath{-}}}^{3}$He; 2D)=-0.88\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}5}$ K and EB{E}_{B}EB​(3{(}^{3}(3He${\mathrm{\ensuremath{-}}}^{4}$He; 2D)=-3.38 mK.
We compute spin diffusion in a dilute Fermi gas at arbitrary temperature, polarization, and strong interaction in the normal phase using kinetic theory. While the longitudinal spin diffusivity ${D}_{\ensuremath{\parallel}}$ depends weakly on polarization and diverges for small temperatures, the transverse spin diffusivity ${D}_{\ensuremath{\perp}}$ has a strong polarization dependence and approaches a finite value for $T\ensuremath{\rightarrow}0$ in the Fermi liquid phase. For a 3D unitary Fermi gas at infinite scattering length, the diffusivities reach a minimum near the quantum limit of diffusion $\ensuremath{\hbar}/m$ in the quantum degenerate regime and are strongly suppressed by medium scattering, and we discuss the importance of the spin-rotation effect. In two dimensions, ${D}_{\ensuremath{\perp}}$ attains a minimum at strong coupling $\ensuremath{-}1\ensuremath{\lesssim}\mathrm{ln}({k}_{F}{a}_{2D})\ensuremath{\lesssim}1$ and reaches ${D}_{\ensuremath{\perp}}\ensuremath{\sim}0.2...\phantom{\rule{0.16em}{0ex}}0.3\phantom{\rule{0.16em}{0ex}}\ensuremath{\hbar}/m$ at large polarization. These values are consistent with recent measurements of two-dimensional ultracold atomic gases in the strong coupling regime.
The quantum second virial coefficient B[Formula: see text] of 3He[Formula: see text] gas is determined in the temperature range 0.001–4 K from the Beth–Uhlenbeck formula. The corresponding phase shifts are calculated from the Lippmann–Schwinger equation using a highly-accurate matrix-inversion technique. A positive B[Formula: see text] corresponds to an overall repulsive interaction; whereas a negative B[Formula: see text] represents an overall attractive interaction. It is found that in the low-energy limit, B[Formula: see text] tends to increase with increasing spin polarization. The compressibility Z is evaluated as another measure of nonideality of the system. Z becomes most significant at low temperatures and increases with polarization. From the pressure–temperature (P–T) behavior of 3He[Formula: see text] at low T, it is deduced that P decreases with increasing T below 8 mK.
Spin polarized gases such as H↑ or 3He↑ can propagate damped spin waves at low temperatures; their origin is the so-called « identical spin rotation effect » in collisions between identical particles. We report here the observation of such effects in 3He↑ in the temperature range 2 < T < 6 K, and preliminary measurements of the coefficient μ which characterizes the quality factor of the spin oscillations. The measurements are in agreement with the numerical calculations of C. Lhuillier.