Perspectives of the theory of spin-polarized quantum systems: Beyond the standard Boltzmann equation

Problems and the latest achievements in the theory of spin-polarized quantum systems are briefly discussed. The current agreement with the experimental data is quite good, but the further improvement of the accuracy of theory is hindered by fundamental problems of the kinetic theory. One of the main goals was to go beyond the simplest Boltzmann equation and a rederivation of the improved versions of this equation for different polarized systems with the emphasis on virial, non-local and non-exchange terms. Some specific applications and boundary effects are presented. The basic problem for polarized dense Fermi-liquids is an applicability of the Landau theory to transverse phenomena. For dilute degenerate systems (e.g., low-temperature liquid mixtures of helium isotopes) the problem is how to go beyond the lowest approximations in density/interaction. Most of the attempts in this direction, especially with regard to superfluid transition in helium mixtures are still unconvincing; this transition remains one of the most intriguing problems of (ultra) low-temperature physics. (orig.)