Computer studies of a dependence of equilibrium state structure on a number of particles for a two-dimensional system of charged particles confined in a disk potential

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Abstract

The problem of finding equilibrium configurations of one-component charged particles, induced by externalelectrostaticfieldsinplanarsystems,isasubjectofactivestudiesinfundamentalaswellinexperimental investigations. In this paper the results of numerical analysis of the equilibrium configurations of charged particles (electrons), confined in a circular region by an infinite external potential at its boundary are presented. Equilibrium configurations with minimal energy are searched by means of special calculation scheme. This computational scheme consists of the following steps. First, the configuration of the system with the energy as close as possible to the expected energy value in the ground equilibrium state is found using a model of stable configurations. Next, classical Newtonian molecular dynamics is used using viscous friction to bring the system into equilibrium with a minimum energy. With a sufficient number of runs, we obtain a stable configuration with an energy value as close as possible to the global minimum energy value for the ground stable state for a given number of particles. Our results demonstrate a significant efficiency of using the method of classical molecular dynamics (MD) when using the interpolation formulas in comparison with algorithms based on Monte Carlo methods and global optimization. This approach makes it possible to significantly increase the speed at which an equilibrium configuration is reached for an arbitrarily chosen number of particles compared to the Metropolis annealing simulation algorithm and other algorithms based on global optimization methods

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1. Introduction The question of how charged particles arrange themselves in a restricted planar geometry attracted continuous attention for many decades (for a review see Ref. [1]). Modern technology allows us to study such phenomena on the same scale, from Bose condensates with some thousand atoms to quantum dots with a few electrons, providing rich information about specific features of correlation effects in mesoscopic systems (see, for example, Refs. [2, 3]). However, finding the exact analytical equilibrium charge distribution (the one that makes the body an equipotential) is not a simple problem. The existence of the symmetry for considered system may simplify the task. Thomson was the first to suggest an instructive solution for interacting electrons, reducing the 3D harmonic oscillator confinement to a circular (2D) harmonic oscillator [4]. He developed an analytical approach, which enables us to trace a self-organization for a small number of electrons (
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About the authors

Eduard G. Nikonov

Joint Institute for Nuclear Research; Dubna State University; HSE University

Email: e.nikonov@jinr.ru
ORCID iD: 0000-0001-7162-0344
Scopus Author ID: 6603099928
ResearcherId: C-4841-2016

Doctor of Physical and Mathematical Sciences, Head of Sector MLIT JINR

6 Joliot-Curie St, 141980, Dubna, Russian Federation; 19 Universitetskaya St, Dubna, 141980, Russian Federation; 34 Tallinskaya St, Moscow, 123458, Russian Federation

Rashid G. Nazmitdinov

Joint Institute for Nuclear Research; Dubna State University

Email: rashid@theor.jinr.ru
Doctor of Physical and Mathematical Sciences, Leading Researcher BLTP JINR 6 Joliot-Curie St, 141980, Dubna, Russian Federation; 19 Universitetskaya St, Dubna, 141980, Russian Federation

Pavel I. Glukhovtsev

Dubna State University

Author for correspondence.
Email: pavelgl2018@gmail.com
ORCID iD: 0009-0005-6424-4455

Master’s degree student of Department of distributed information computing systems of Dubna State University

19 Universitetskaya St, Dubna, 141980, Russian Federation

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Copyright (c) 2024 Nikonov E.G., Nazmitdinov R.G., Glukhovtsev P.I.

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