Work

The series of research papers is devoted to the study of the properties of deformed oscillators and their application to nonlinear systems of quantum physics. The author classified the deformed oscillator models. That was very important, because of nowadays there exist a great number and diversity of deformed oscillators. Rebesh A.P. also proposed new interesting models and specify their location in the existing hierarchy of the known models. There is the parameter (or parameters) of deformation in the commutation relations of deformed oscillators so they have unusual properties in comparison with the ordinary quantum harmonic oscillator. The author examined the energy spectra of many deformed oscillators and found out that they have the energy level degeneracity. On the set of deformed oscillators the deformed analogs of Bose gas model were elaborated. In such models the volume of particles, their internal structure or interparticle interaction are effectively taken into account. Within the p,q-analog of Bose gas model (p,q-Bose gas) for free non-relativistic particles the virial coefficients (the first five) of the virial expansion of the equation of state were obtained. It is important that the virial coefficients contain the deformation parameters p and q. By change the deformation parameters one can change the effective interparticle interaction. Therefore, the equation of state of p,q-deformed Bose gas model can better describe real quantum gases. The critical temperature of condensation of p,q- Bose gas was also obtained and it turned out to be higher than the critical temperature of Bose gas. The model of μ-Bose gas was introduced. In the framework of such model theintercepts of two- and three-particle correlation functions were evaluated. Also it was obtained the exact formulas for asymptotics of intercepts (as a functions for the parameter μ) at large momenta. There is a good agreement between theoretical results and data for the correlations of π-mesons obtained in the experiments on relativistic nucleus-nucleus collisions (STAR / RHIC).