Деякі властивості генератора ланцюжка рівнянь Боголюбова одновимірної системи виділеної частки в термостаті

Abstract

Установлено властивості генератора ланцюжка рівнянь Боголюбова одновимірної несиметричної системи виділеної частки в термостаті.; One of the problems which is of great current relevance in modern mathematical physics is the study of the real processes which occur in different macro-spaces based on the properties and laws of motion of the microparticles of which they are composed. The study of infinite systems – systems with an infinite number of particles ― is very interesting. These systems are considered in terms of infinite phase space. Their condition is completely described by the sequence of particle distribution functions. The evolution of the system is considered to be certain, if from the known initial state of the system it is possible to define its state at some arbitrary moment in time. This evolution is described by the Cauchy problem for Bogolyubov's chain of equations – the infinite system of integro-differential equations (BBGKY hierarchy). The BBGKY hierarchy is seen as an abstract evolution equation for a given space of distribution functions. In order to find a solution it is necessary to construct an evolutional operator for the distribution function. This article is devoted to the infinite one-dimensional non-symmetrical system of particles interacting via the hard-core potential. The properties of the generator of the Bogoliubov equations chainlet for the one-dimensional nonsymmetrical system of a highlighted part of a thermostat are derived.