Peletmynskiy O. Spontaneous symmetry breaking in Bose and Fermi systems and spatially periodic states

Subject of study: ordering phenomena in a weakly non-ideal Bose gas below the condensation point and Fermi liquid. Objective: development of microscopic theory of spatially periodic states in a Bose condensate within a weakly non-ideal Bose gas model; theoretical investigation of Fermi liquid phase transitions from the normal state to the spatially periodic and to the state with a broken isotropy in the momentum space. Methods: quasi-average method, separated condensate method, principle of local statistical equilibrium, Landau-Silin Fermi liquid approach, variational principle. Theoretical and practical results, novelty: Thermodynamics and nondissipative hydrodynamics of spatially periodic condensate are constructed. Expressions for transition temperatures and order parameters in a Fermi liquid are obtained. Field of application: physics of quantum liquids and phase transitions.