Bulakhov M. The role of non-local interaction in ultracold Bose gases with consideration of spin degrees of freedom

The dissertation is devoted to studing the effect of the nonlocality of interaction on: first, thermodynamic quantities of a weakly interacting Bose gas both in the upper neighbourhood of the transition temperature (higher, but close to it) to the state with Bose-Einstein condensate (BEC) and in the state with BEC at zero temperature; second, spin-related effects and the structure of the single-particle excitation spectrum of a weakly interacting Bose gas of spinless or spin-1 atoms with BEC at zero temperature. Chapter 1 deals with the presentation of the basic approaches and the reference point of the author’s research: thermodynamic perturbation theory, Bogoliubov theory of a weakly interacting Bose gas, and generalization of Bogoliubov canonical transformation. Chapter 2 is devoted to the constructing thermodynamics of a Bose gas in the upper neighbourhood of the phase transition temperature to the state with BEC taking into account the first and second order corrections in interaction to the main thermodynamic quantities. The theoretical description is based on the thermodynamic perturbations theory. The results are analyzed by using numericalmethods for local and non-local models of the interaction potential. Chapter 3 analyzes the system of equations that allows one to determine such thermodynamic characteristics of a weakly interacting ultracold Bose gas of spinless atoms with BEC as chemical potential and condensate particles density. It involves the contribution of quadratic terms in the creation and annihilation operators and enables to study the system for a number of model non-local interaction potentials. The complete analysis was carried out by employing the numerical methods for two models of non-local interaction potential: a model of semitransparent spheres and a model with Gauss (normal) distribution profile. In Chapter 4 the author explores thermodynamics and magnetic properties of all possible magnetic states of a Bose gas of spin-1 atoms with BEC in the presence of an external magnetic field. In contrast to previous studies of spinor condensates, the interatomic interaction is considered to be non-local. In this case, the corresponding Hamiltonian must be constructed taking into account the spin and quadrupole degrees of freedom, which are elegantly introduced on an equal footing through the prism of the SU(3) algebra. The coupling with the external magnetic field is provided both by the spin operator (the linear Zeeman effect) and by the quadrupole moment operator (the quadratic Zeeman effect).