Tarasov A. Generalized Fermi-liquid approach in the theory of superfluidity of 3He and neutron matter with anisotropic spin-triplet pairing in strong magnetic fields.

Tarasov A.N. Generalized Fermi-liquid approach in the theory of superfluidity of 3He and neutron matter with anisotropic spin-triplet pairing in strong magnetic fields. The Doctoral Thesis is devoted to theoretical investigation of equilibrium properties and phase transitions in superfluid Fermi-liquids (SFLs) with spin-triplet pairing of electrically neutral fermions in strong magnetic fields. The superfluid phases of liquid helium-3 and phases of dense neutron fluid in cores of neutron stars serve as examples of such SFLs. Based on the Fermi-liquid approach generalized to superfluid systems, in the first part of the thesis, consisting of two chapters, the results are obtained for superfluid phases of liquid helium-3 in moderately strong magnetic fields at temperatures near the phase transition temperature from normal to superfluid state and also for any temperatures at which helium-3 is superfluid. In particular, a refined formula is obtained for the phase transition (PT) temperature from superfluid phase 3He-A to phase 3He-B in moderately strong magnetic field with new additional correction which is nonlinear in field. General explicit expressions are derived for abnormal and normal distribution functions of quasiparticles, which are valid for description of arbitrary phases of the neutral paramagnetic SFL with spin-triplet pairing of the 3He type at any temperatures in a static and uniform magnetic field. The second part of the thesis (see chapters 3, 4, 5) is devoted to investigation of dense superfluid spatially homogeneous pure neutron matter (SNM) with spin-triplet anisotropic p-wave pairing of the 3He-A1,2 type in static and spatially uniform moderately strong magnetic field. The effective Skyrme forces (which depend on density of neutron matter) are used as interaction in SNM. General approximate analytical formulas for phase transition temperatures in spatially uniform pure NM (with arbitrary parametrization of the effective Skyrme forces) from normal to superfluid states with spin-triplet p-wave pairing of 3He-A1,2 type are obtained. These PT temperatures are functions linear of moderately strong magnetic fields and nonlinear of number density of neutrons in the range from sub- to supra-nuclear densities. The paramagnetic susceptibility of SNM with traditional parametrizations of Skyrme forces (with only one term dependent on neutron density) is divergent at critical value of density, which, as a rule, exceeds the nuclear density. It might be explained as phase transition of SNM to ferromagnetic state which coexists with anisotropic spin-triplet superfluidity in neutron matter with traditional Skyrme forces. In the subsequent chapters 4 and 5 the superfluid and magnetic properties of SNM in the state of statistical equilibrium are investigated with using a number of new generalized effective Skyrme forces from the family of BSk parametrizations, which contain three terms dependent on neutron density. It was found that the temperature dependencies of the energy gap of superfluid Fermi-liquid of the 3He-A type near zero temperature and in the vicinity of PT temperature Tc0(n) (in the absence of a magnetic field) are determined only by the symmetry of the order parameter and do not depend on the nature of interactions, which give rise to the triplet Cooper pairing in a system. The improved approximate analytical formulas are derived for the specific heat of SNM (or SFLs) with anisotropic triplet p-wave pairing of the 3He-A type, which are valid near zero temperature and in the vicinity of PT temperature Tc0(n). The character of the specific heat dependence on temperature T in a superfluid phase appears not to be dependent on the type of interaction between fermions. This means that the power-law temperature dependence of the specific heat of SNM (or SFLs) is determined by the type of unconventional anisotropic Cooper pairing of fermions. It is established that the dependence of the specific heat on the density differs significantly for various SFLs (or for SNM with different generalized parametrizations of Skyrme forces) and is determined by the interaction parameters.