Spin diffusion in dilute, polarized 3He-4He solutions

Abstract

Spin d~namics for arbitrarily polarized and very dilute solutions of 3He in liquid He are described. We began at a very fundamental level by deriving a kinetic equation for arbitrarily polarized dilute quantum systems based on a method due to Boercker and Dufty. This approach allows more controlled approximations than our previous derivation based on the Kadanoff-Baym technique. Our previous work is here generalized to include T-matrix interactions rather than the Born approximation. Spin hydrodynamic equations are derived. The general equations are valid for both Fermi and Bose systems. By use of a well-known phenomenological potential to describe the 3He-JHe Tmatrix we calculate longitudinal and transverse spin diffusion coefficients D_L and D/I and the identical-particle spin-rotation parameter ~t. We confirm that these two diffusion constants differ at low T with DI approaching a constant as T ~ O, and D H ~ lIT 2. Estimates of errors made by our approximations are considered in detail. Good agreement is found in comparison with data from both Cornell University and the University of Massachusetts. We find that the s-wave approximation is inadequate and that mean-field corrections are important. Comparison is also made between theory and the recent UMass viscosity measurements.

Transverse spin dynamics in a spin-polarized Fermi liquid

“…The latter is essentially simplified when both the temperature T and the polarization γH are much smaller than Fermi energy ε F and the momenta of all excitations are confined to lie in the vicinity of both Fermi surfaces and therefore one may decouple the angular and energy variables in the collision integral in the manner first introduced by Abrikosov and Khalatnikov 2 . We confirm the results of the papers [7][8][9][10] where the same problem were treated for the dilute Fermi gas. It is found in particular that at finite polarization spin-wave damping has a finite value at T = 0.…”

“…However, in the presence of finite polarization a dissipative transverse diffusion motion is also present. Corresponding relaxation time does not diverge at zero temperature [7][8][9][10][11] and transverse spin waves attenuate at T = 0. The calculations of transverse spin-diffusion coefficient D ⊥ have been done in dilute degenerate Fermi gas with arbitrary polarization at T = 0 in the papers by W.Jeon and W.Mullin 7 , A.Meyerovich and K.Musaelian 8 , and at T = 0 in the article 9 .…”

“…Corresponding relaxation time does not diverge at zero temperature [7][8][9][10][11] and transverse spin waves attenuate at T = 0. The calculations of transverse spin-diffusion coefficient D ⊥ have been done in dilute degenerate Fermi gas with arbitrary polarization at T = 0 in the papers by W.Jeon and W.Mullin 7 , A.Meyerovich and K.Musaelian 8 , and at T = 0 in the article 9 . A derivation and an exact solution of the kinetic equation in the s-wave scattering approximation for dilute degenerate Fermi gas with arbitrary polarization at T = 0 and for a small polarization µH ≪ ε F at T = 0 have been obtained also in the papers by D.Golosov and A.Ruckenstein 10 .…”

“…However, besides the reactive part the total spin current calculated in presence of collisions includes dissipative or spin-diffusion part resulting in imaginary part of dispersion law for the transverse spin waves. At the microscopic level the collisions treatment is equivalent to derivation of kinetic equation that was done for the case of spin-polarized diluted Fermi gas [7][8][9][10] . Being addressed to the same problem in polarized Fermi-liquid, we need the kinetic equation.…”

Crossover from collisionless to collisional spin dynamics of polarized fermions

“…In the strongly interacting collisional regime, the dynamics are governed by spin diffusion. These two regimes have been studied experimentally and theoretically in cold atoms [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15], liquid helium [16][17][18][19], and solid state systems [20][21][22].…”