Transport properties in a spin polarized gas, I

Abstract

Résumé.-On étudie l'influencedes effetsd'indiscernabilitédes atomes sur les propriétés de transport dans un gaz orienté à basse température, 3HeÎ par exemple, le gaz étant supposé dilué et donc non dégénéré. Dans ce but, on commence par étudier en détail ces effets dans une collision binaire; bien que l'on néglige toute interaction agissant sur les spins pendant la collision, on constate que des effets d'interférence quantique peuvent conduire à des changements de leur orientation (effets de rotation de spins identiques). Dans une seconde étape, on écrit une équation de Boltzmann satisfaite par un opérateur densité de spin ps(r, p), qui joue un rôle analogue à la fonction de distribution classique de Boltzmann f(r, p), et peut être obtenu par transformation de Wigner de l'opé-rateur densité à une particule; dans cette équation, les effets d'indiscernabilité introduisent trois nouvelles « sections efficaces» indépendantes, alors que le terme classique ne dépend que d'une seule. L'application de la méthode de Chapman-Enskog à l'ordre le plus bas introduit alors un opérateur linéaire de collision Fe qui dépend explicitement de l'orientation M du gaz; en particulier, si M n'est pas nul, Fe n'est pas hermitique. Enfin, les résultats précédents sont appliqués à deux cas particuliers,conduction de la chaleur et viscosité, et l'on obtient la dépendance des coefficients correspondants en fonction de M. Cette dépendance peut être très marquée à basse température. Dans l'article qui suit celui-ci, on étudie le problème de la diffusion de spin et l'on prédit un certain nombre d'effets quantiques dus à l'indiscernabilité des particules: équation de diffusion anisotrope, non linéaire, couPlage avec un gradient thermique.Abstract. -The transport properties of a spin polarized gag at low temperature eHeÎ for instance)are studied, the emphasis being put on the particle indistinguishability effects during collisions; the gas is dilute and no degeneracy effects occur. We first study in detail the,partic1e indistinguishability effects in a binary collision and, although all interactions involving the spins are completely ignored during the collision time, we note that interference effects can lead to a change of the spin directions «< identical spin rotation effect »). From this study, we obtain the collision term of a Boltzmann equation for a spin operator ps(r, p), which is the analogue of a classical Boltzmann distribution function fer, p), and can be obtained by a Wigner transform -with respect to the orbital variables -of the one particle density operator; in this Boltzmann equation, in addition to the classical term which depends on one cross section, several terms arise from partic1e indistinguishability effects and introduce 3 other, independent, «cross sections ». The c1assical Chapman-Enskog approximation is then used and a linearized collision operator Fe is 0btained ; r cdepends on the spin polarization M in the gas and, if Mis not zero, r c is not a Hermitian operator. Final1y, the preceding results are applied to two ...

Spin rotation effects and spin waves in gaseous 3He↑

“…These predictions have been confirmed in experiments with liquid 3He at very low temperatures (7" ~ 10 mK) and used to measure the Fermi liquid interaction parameter A for pure 3He and 3He-4He mixtures [13]. For spin-polarized dilute gases the situation is rather different, and no phenomenological parameter has to be introduced in the theory [7,14], so that all transport properties (heat conduction, viscosity, spin waves) can be calculated ab initio from the interatomic potential (1). This has been done recently by C. Lhuillier for HT.…”

Cumulative Identical Spin Rotation Effects in Collisionless Trapped Atomic Gases

“…Spin waves in dilute gases were predicted at the beginning of the eighties [1,2] and confirmed experimentally soon after [3,4,5]. They can be understood in two equivalent ways, either as a consequence of spin mean field [1], or in more microscopic terms as the cumulative result of the identical spin rotation effect (ISRE) -an effect taking place during binary collisions between identical atoms [2].…”

“…On average, an atom oscillates 700 times in the axial trap between two collisions. We base our analysis on the formalism used in [2] and [8], which gives a general frame for the study of non de-generate quantum gases. It distinguishes two effects of the interactions: mean field effects (forward scattering in collisions) and "real" collisions (lateral scattering), both with a full treatment of the effects of spin polarization and statistics.…”

“…In the latter, the peak density n(0) and the typical scattering length a 12 are respectively 15 and 20 times smaller than in the JILA experiment, making the diluteness factor 1/n(0)a 3 12 of the gas 10 5 times larger. The differences can be expressed in terms of 5 relevant time scales: (1) the radial trap period 2π/ω rad ; (2) the axial trap period 2π/ω; (3) the average time between (lateral) collisions τ ∼ (4πa 2 12 n(0)v T ) −1 , where v T ≡ k B T /m is the thermal velocity, T the temperature and m the atomic mass; (4) the typical spin precession period in the external magnetic field 2π/|Ω 0 |; and (5) the typical precession period in the spin mean-field τ f wd ∼ m/ |a 12 |n(0). These time scales [ where a 12 ∼ −5a 0 and Ω 0 /2π ≈ −10 Hz are typical values for the Duke exp.…”

“…They can be understood in two equivalent ways, either as a consequence of spin mean field [1], or in more microscopic terms as the cumulative result of the identical spin rotation effect (ISRE) -an effect taking place during binary collisions between identical atoms [2]. Similarly, the Faraday effect is a rotation of the spin of photons that can be seen, either as a consequence of a macroscopic index of refraction, or as resulting from the accumulation of microscopic forward scattering events between photons and atoms.…”