Construction of theory of a binary mixture of nonideal Bose gases (or liquids) by the method of collective variables I. Wave function and ground-state energy, excitation spectrum, correlation functions, thermodynamics of the system at $T=0$

For a binary mixture of nonideal Bose gases (or liquids) the method of collective variables is used to find the energy and wave function of the ground state and the excitation spectrum. The density-density correlation functions are calculated, and the thermodynamics of the system at $T=0$ is considered. In the case of a binary mixture of gases with equal masses of the particles it is established in the framework of the model with “pseudopotential of hard spheres” that separation of the mixture into components does not occur in two cases: low density of the mixture and any concentration of the admixture or any density and a low concentration of the admixture. The possibility of a superfluid state is stablished. The system is also investigated by the variational method. The application of the theory to real binary Bose mixtures, for example $\operatorname{He}^4$ and $D_2$ or $\operatorname{He}^4$ and $\operatorname{HT}$ is discussed.