## Scientific Bulletin. Physical and Mathematical Research

#### Article Title

#### Abstract

In this paper, multi-variety densely packed par-ticle dynamic systems with the ability to interact with the shielded Yukawa potential were studied. Also, in order to study more widely the dynamics of systems containing particles interacting via shielded potential, the theoretical foundations of the dynam-ics of systems consisting of an arbitrary number of bounded - sorted multi-particles are analyzed. The dynamics of an arbitrary number of interacting par-ticle systems on a screening potential was studied using the Bogolyubov-Born-Green-Kirkwood-Yvon (BBGKY) chain of quantum kinetic equations. The BBGKY chain of quantum kinetic equations has solutions for the case that characterizes the evo-lution of the same particle system depending on a certain distance between interacting particles, and is shown and determined to be unique. In this case, the electric charge and mass of particles were assumed to be dependent on the particle type. It is known that when the particle velocity is small, the problem is considered within the framework of non-relativistic quantum theory, and the evolution of particles of such a system is described by the BBGKY chain of quantum kinetic equations.

BBGKY used the semi-group method to find a solution of the chain of quantum kinetic equations that satisfies the initial condition, i.e. to solve the Cauchy problem. The theorem on the self-adjoint of the operator, which represents the shielded potential, was also used effectively in determining the solution. It is known that in nuclear physics, the Yukawa po- tential (the potential that determines the interaction between protons and neutrons) is used as a shielded pendant potential to estimate the modified ion po- tential, i.e., modified.

The problem of the interaction of electrolyte ions in liquid solutions was studied in 1923 by P. Debay and E. Hückel. They proposed to determine the interaction potential of electrolyte ions using shielded potentials. For this reason, in the scientific literature, such potentials are referred to as Debye- Hückel potentials.

In the Debay-Hückel potential, the interaction of ions with the central ion and the ions forming the ionic sphere around it is accepted. The ion coeffi-cient of activity was determined using such interac-tions. In cases where the system parameters do not change over time, the Debay-Hückel laws corre-spond to the conditions of thermodynamic equilib-rium. Later, the Debye-Hückel laws led to the devel-opment of plasma physics. It is known that plasma is often or constantly composed of ionized gas, neu-tral atoms, and charged particles (ions and electrons). Therefore, in the evaluation of processes in plasma, the distance of exposure of the shielded pendant field charges, called the Debye-screening radius, is of great importance. In recent times, interest in the dynamics of interacting multi-particle quantum sys-tems on non-equilibrium sate with the shielded Cou-lomb potential has significantly increased. The study of such systems is still important and signifi-cant in the exploration of the non-equilibrium dy-namic properties of multi-body systems. To date, the study of the dynamics of interacting shielded poten-tial system particles has been conducted on systems consisting of two or three particles. This study, un-like other studies in this area, studied the dynamics of systems consisting of an arbitrary number of freely bounded-sorted multi-particles. To study the dynamics of an arbitrary number of interacting par-ticle systems on a shielded potential, a chain of quantum kinetic equations of Bogolyubov-Born-Green-Kirkwood-Yvon (BBGKY) was used.

#### First Page

63

#### Last Page

69

#### References

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#### Recommended Citation

Bogolyubov, N.N.; Mukhayo, Rasulova; and Avazov, U.O.
(2021)
"Evolution of quantum systems consisting of mul-tiple various particles interacting with general-ized yukasha potential,"
*Scientific Bulletin. Physical and Mathematical Research*: Vol. 3
:
Iss.
1
, Article 10.

Available at:
https://uzjournals.edu.uz/adu/vol3/iss1/10