МОДЕЛИРОВАНИЕ ИЗЛУЧЕНИЯ В МИКРОСИСТЕМАХ С ПОМОЩЬЮ ЦЕПЕЙ МАРКОВА

Abstract

To solve important problems related to radiation in microsystems, the methods of quantum electrodynamics are successfully used. At the same time, a number of problems remain (vacuum energy, divergence in local interaction, the physical meaning of the fine structure constant) that cannot be resolved within the framework of this theory. Therefore, an urgent task is to develop alternative mathematical models that can be additionally used to study the radiation process in microsystems. In this work, to model the radiation process in microsystems, Markov processes with continuous time and discrete states are used. The mathematical model is based on Heisenberg's uncertainty principles and conservation laws. The main mathematical tools are Kolmogorov graphs and their corresponding systems of equations. The key idea is that the phase space of a particle is discrete. The model of the discrete phase space is distinguished by its comparative simplicity and efficiency, and allows applying the well-developed theory of Markov processes to the phenomena under study. The scale of the model and its discrete structure make it possible to avoid irremovable singularities. The article presents: an original physical interpretation of the fine structure constant, a stochastic analogue of the redshift law and the magnitude of the Schwarzschild gravitational radius, a stochastic interpretation of the fine structure constant of the gravitational field is proposed. A comparative analysis of the fine structure constants for the gravitational and electromagnetic fields has been carried out.