Karpenko V. Phase transitions in dense systems of interacting Bose particles

The dissertation is devoted to the study of phase transitions and thermodynamic properties of interacting boson systems consisting of particles and antiparticles at nonzero isospin densities. The focus is on -meson systems, which serve as a natural model for studying strongly interacting matter at high densities and temperatures characteristic of processes in the early universe, neutron stars, and relativistic heavy ion collisions. The relevance of the topic is determined by the need for a deeper understanding of the phase structure of hadronic matter, in particular the behavior of meson systems at finite temperatures and isospin densities. Pions, as the lightest hadrons with nonzero isotopic charge, are ideal objects for studying Bose-Einstein condensation phenomena under conditions of strong interaction. Theoretical and experimental studies indicate that under certain conditions, -mesons can form a Bose condensate, which potentially affects the evolution of dense hadronic matter. The aim of this work is to construct a consistent thermodynamic model capable of describing the behavior of a multicomponent boson system over a wide range of temperatures and densities, taking into account repulsive and attractive interactions between particles. The main results of the work are as follows: • A self-consistent thermodynamic model of the mean field for a system of interacting -mesons has been developed, taking into account repulsion and attraction, suitable for describing both Bose condensation and liquid-gas phase transitions. • The modes of “weak” and “strong” attraction between pions, which determine the type of phase transitions present, have been separated: second order for weak interaction and first order for strong interaction. • The presence of phase transitions in a model system consisting of a combination of different types of pions, which can affect only one of the components, is shown. • A “virtual” second-order phase transition without the formation of an order parameter is described. • The possibility of double condensate formation is shown, and that the double condensate of particles and antiparticles exists at zero chemical potential. • Generalized Maxwell rules and phase diagrams of the system are constructed, which take into account the presence of condensate and a “liquid-gas” phase transition. • The limits of applicability of the canonical and grand canonical ensembles are discussed, and it is shown that the latter is incorrect in the condensate phase. • A modification of the model by adding electrical interaction is proposed, and the influence of electrical interaction on the thermodynamic characteristics of the system is evaluated. Although the research is theoretical in nature, its results can be applied to: • modeling hot and dense hadronic matter in heavy ion collisions (LHC, RHIC); • analyzing the states of matter in neutron stars; • constructing cosmological models of the early universe; • further developing effective theories of strong interaction (QCD) at low energies. The work has formed a consistent theoretical picture of phase transitions in systems of interacting bosons at nonzero isospin densities. The effects identified (double condensate, virtual transition, and specific behavior of ensembles) constitute an important contribution to statistical physics and the theory of strongly interacting matter. The developed model can serve as a basis for further research on multicomponent boson systems and their applications in high-energy physics and astrophysics.