Mean-field and spin-rotation phenomena in fermi systems : the relation between the leggett-rice and lhuillier-laloë effects

K. Miyake , W.J. Mullin , P.C.E. Stamp

The term in the Boltzmann equation collision integral causing identical-particle spin rotation in the Lhuillier-Laloë (LL) theory of a non-degenerate quantum gas is shown to be equivalent in the dilute limit to the molecular field precessional term giving rise to the Leggett-Rice (LR) effect in a degenerate Fermi system. This equivalence is shown (a) by considering the spin-rotation term at low temperatures and (b) by deriving hydrodynamic equations valid for all temperatures from the Landau-Silin equation in the s-wave approximation. The spin-rotation factor μ resulting from (b) is found to agree with the LR value at low temperatures and with the LL value at high temperatures. The diffusion constant Do that results has the proper low temperature behaviour, including the standard mean-field correction factor ; at high temperatures Do has the LL form times a the mean-field correction factor. The importance of the missing mean-field term is illustrated by showing that it gives rise to second virial corrections to the pressure.

Mots clés: Boltzmann equation; fermion systems; spin dynamics

Domaines: Articles anciens

K. Miyake, W.J. Mullin, P.C.E. Stamp. Mean-field and spin-rotation phenomena in fermi systems : the relation between the leggett-rice and lhuillier-laloë effects. Journal de Physique, 1985, 46 (5), pp.663-671. ⟨10.1051/jphys:01985004605066300⟩. ⟨jpa-00210006⟩