Kinetic equations for neutral Fermi liquids in DC magnetic fields. The nonlinear and particle-hole asymmetric effects

Since nonlinear effects are of the same importance as the particle-hole asymmetry (PHA) effects for normal Fermi liquids, at least for some physical situations, a formalism is presented taking both into account. Moreover, because the nonlinearity or PHA is easiest to induce by strong magnetic fields, weak polarization effects are also included. The kinetic equations for the weakly coupled density and magnetization modes are obtained under these circumstances. They lead to an additional effective mass equation in comparison to the Landau formula, joining the suitable angular average of the effective interaction of triples of quasiparticles with the gradient of the two-quasiparticle interaction with PHA effects included. The equations are investigated in detail for ac magnetic field much smaller than the dc field in two cases: (1) at almost equilibrium magnetization of the sample and (2) at almost equilibrium (in the length) magnetization precessing around a dc field tipped to it by an angle # 0. In the first case, the coupling of the longitudinal magnetization to the density modes should lead to a rather detectable excitation of the zero sound by the ac field longitudinal with respect to the dc field. In the second case, the coupling of the spin waves of the magnetization, transverse with respect to the tipped magnetic moment, to the zero sound by virtue of the polarization effects could lead to the interesting effects discussed. Moreover, the possibility of second harmonic generation in the zero-sound channel by the ac field in the nonlinear regime is also noted.