Naumovets A. Description of the thermodynamic properties of crystals and superfluid helium, taking into account external fields and the interaction of quasiparticles

This thesis is devoted to theoretical research of the properties of quasiparticles systems in solids at high and low temperatures, and in superfluid helium in the presence of an external electric field. For a crystal of arbitrary symmetry, the fourth order tensors of elastic moduli has more than six thousand elements, of which 126 (for the least symmetric triclinic crystals) are independent. To simplify the description of the elastic properties of crystals, a model of an isotropic medium equivalent to the properties of real crystals is developed. The fourth-order elastic moduli of this medium are obtained. A nine-constant model for describing a solid is constructed. The value of the anisotropy parameter of the crystal lattice is calculated for various substances of cubic crystal system. Different behavior of the heat capacity at high temperatures was revealed depending on the sign of the anisotropy parameter. At low temperatures, a hydrodynamic regime is established in the phonon gas of the crystal lattice, and the thermal conductivity coefficient has a maximum. The possibility of the propagation of weakly damped heat waves occurs. The region of existence of the second sound waves in crystals of diamond and lithium fluoride is calculated. The contributions to the phonon lifetime from normal processes, umklapp processes, scattering on isotopes and boundaries of a solid are determined. The case when normal processes predominate is considered. In the thesis, it is proved that the properties of the quasiparticles– rotons – play main role in electrical activity of superfluid helium, when the components of He-II are in relative motion. Equations of two-fluid hydrodynamics of superfluid helium accounting an external electric field are found. The polarization vector due to the dipole moments of rotons is calculated.