Discrete model of the evolution of the phase space of fractionally dimensional microsystems

The study of the process of changing information in microscopic systems is a rather complex and urgent scientific problem. The difficulty lies in the fact that, due to the microscopic nature of objects, it is impossible to use well-known thermodynamic methods based on the laws of large numbers. One of the possible methods for studying microscopic systems is the use of discrete Markov models with continuous time. Such models are based on the Heisenberg uncertainty principle and adequately describe the interaction between a macroscopic observer and a microscopic system at a quasi-classical level. At the same time, the use of semiclassical models makes it possible to avoid singularities, including those that cannot be eliminated, arising at small distances and high energies. In this paper, a discrete mathematical model of the phase space of an elementary particle will be used to study microscopic objects with a dimension of n=1. As a result of using the model, an original interpretation of the quark structure of hadrons was obtained. In particular, the dynamics of the functioning of quarks in the proton and neutron, the conditions for the formation of Δ resonances (Δ0, Δ+, Δ+, Δ++) are presented. The problem of the absence of free quarks (the phenomenon of confinement) is also considered. The paper considers only the first generation of quarks and the hadrons based on them. On the basis of known experimental data, numerical calculations have been carried out, showing sufficient adequacy of the model. The mathematical model of the discrete phase space, created to study the evolution of information in microscopic systems, is applicable to solving problems of elementary particle physics and can, in some cases, supplement the existing models of the quark structure of hadrons.