Transport properties in a spin polarized gas, II

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 Mare 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 ofM 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. ln 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. Introduction.ln the preceding article, we have studied the consequences of particle indistinguishabilitY effects on the collision term of the Boltzmann equation for a dilute (non-degenerate) spin polarized gag. We have seen that these effects introduce several terms which have the form of commutators or anticommutators between spin density operators; the former correspond to what we have called the « identical spin rotation effect ». We have also applied our results to the sindy of the heat conduction and viscosity coefficients and found that both may depend strongly on the nuclear polarization M of the gas; the correlations between spin variables and velocities of the atolls have also been discussed. Nevertheless, it so happens that only the anticommutators give a contribution to the viscosity and heat conduction coefficients, the identical spin rotation eITectplaying no foie in both cases. This is because the commutators disappear from the calculations whenever a spin rotation invariance argument ensures that the average spin density operator p~ ahd the solution Ops of the linearized Boltzmann equation can be diagonalized