On présente dans cet article une étude théorique de la relaxation de spin d'un gaz atomique dilué, produite par un gradient de champ magnétique de faible intensité. La théorie est valide à la fois en champ faible ou modéré (cas où le temps de corrélation du gaz qui joue un rôle est le temps de diffusion dans son récipient) et en champ fort (c'est alors le temps entre collisions qui joue le rôle essentiel). Elle tient compte des effets quantiques d'indiscernabilité des atomes. Si les effets de divergence du libre parcours moyen dans un gaz polarisé à température nulle ne jouent ici aucun rôle, contrairement à ce qui se produit pour la viscosité par exemple, les effets de « rotation des spins identiques » peuvent être importants.
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.
A theory of magnetotransport phenomena in low-density paramagnetic systems at low temperature is proposed. The main contentions are based on considering a dissipation mechanism due to the inelastic scattering of paramagnetic particles with transverse collective spin fluctuations. In the presence of an external magnetic field and in the low-momentum limit the corresponding cross section may be very large. Theoretical estimates are in good agreement with recent indirect measurements of intrabeam scattering for cooled H atoms. The extra scattering channel results in a drastic reduction in the mean free path and, consequently, a decrease in the thermal conductivity and viscosity, in contrast to previous theories. In the case of degenerate Fermi systems, the calculations yield quite different temperature dependencies compared with those given by the Fermi-liquid approach. Application of the theory to gaseous H\ensuremath{\downarrow}, $^{3}\mathrm{\ensuremath{\uparrow}}$, and dilute $^{3}\mathrm{\ensuremath{-}}^{4}$He mixtures are briefly discussed, and it is shown that the thermal conductivity and viscosity of gaseous H\ensuremath{\downarrow} under common conditions are expected to be roughly
102 times less than the normal gas-kinetic values.
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.
The longitudinal relaxation time T
sb1 is calculated for a dilute Fermi gas. We include the possibility of arbitrary degrees of polarization P, and uniform external magnetic fields. At low temperatures T
sb1 is proportional to T
sp−2 for the unpolarized gas in agreement with earlier calculations. For a polarized system in zero applied field the separation between up and down Fermi spheres provides an open channel in phase space for spin flipping processes. As temperature is reduced to zero T
sb1 levels off and approaches a constant value which depends sensitively on P, leading to much smaller values of T
sb1 than in the unpolarized case. For relaxation in a uniform external field H, Zeeman energy conservation during spin flipping interactions essentially shifts the location of the T
sp−2 behavior from zero polarization to the polarization P(H) which would be produced in equilibrium with the external field H. When the initial polarization of the system is different from P(H), T
sb1 again approaches a constant value which is equally sensitive to the initial polarization as temperature is reduced to zero. We apply our calculations to the case of dilute
sp3He-HeII solutions. We also consider the calculation of density dependent corrections to T
sb1 for unpolarized, or weakly polarized
sp3He-HeII using the long wavelength limit of the Bardeen-Baym-Pines interaction as a form for the spin independent part of the
sp3He-
sp3He interaction. Owing to the positive sign of the antisymmetric Landau parameter
rmFsbspoa in dilute
sp3He-HeII Fermi Liquid interactions act to screen the magnetic dipole interactions which cause relaxation. To lowest order in density we find that the relaxation rate 1/T
sb1 is reduced by factor
rm(1−3Fsbspoa) which compares favorably with recent calculations of T
sb1 for pure
sp3He.
We examine spin diffusion in a two-component homogeneous Fermi gas in the normal phase. Using a variational approach, analytical results are presented for the spin diffusion coefficient and the related spin relaxation time as a function of temperature and interaction strength. For low temperatures, strong correlation effects are included through the Landau parameters, which we extract from Monte Carlo results. We show that the spin diffusion coefficient has a minimum for a temperature somewhat below the Fermi temperature with a value that approaches the quantum limit ∼ℏ/ m in the unitarity regime, where m is the particle mass. Finally, we derive a value for the low-temperature shear viscosity in the normal phase from the Landau parameters.