[PDF]     http://dx.doi.org/10.3952/lithjphys.50402

Open access article / Atviros prieigos straipsnis

Lith. J. Phys. 50, 405–411 (2010)

E. Anisimovas, O. Rancova, and T. Varanavičius
Vilnius University, Saulėtekio 9, LT-10222 Vilnius, Lithuania

E-mail: egidijus.anisimovas@ff.vu.lt

Received 14 September 2010; revised 27 October 2010; accepted 15 December 2010

We model the formation of ordered structures in systems consisting of up to 52 identical particles interacting by Coulomb repulsion forces and confined within a two-dimensional parabolic trap. Our algorithm consists of a number of Metropolis steps followed by the steepest-descent minimization of the total potential energy of the system. The role of the first (Metropolis) stage is to create a random canonically distributed configuration, while the subsequent minimization locates the closest local minimum starting from this random configuration. In most cases we find that more than one stable configuration may be formed, and often the lowest-energy configuration is not the most probable one. The concept of configurational entropy is introduced to quantify the uncertainty due to the availability of several alternative structures.
Keywords: Wigner crystallization, Monte Carlo simulation, entropy
PACS: 05.20.-y, 61.46.Bc

E. Anisimovas, O. Rancova, T. Varanavičius
Vilniaus universitetas, Vilnius, Lietuva

Tiriamas tvarkingų darinių formavimasis sistemose, sudarytose iš N 6 52 identiškų dalelių, esančių apskritoje dvimatėje gaudyklėje ir tarpusavyje sąveikaujančių Kulono stūmos jėgomis. Skaitmeniniam modeliavimui pasitelkiami Metropolio algoritmas ir greičiausio nusileidimo metodas. Metropolio algoritmo paskirtis yra sugeneruoti atsitiktinę (kanoninio pasiskirstymo) dalelių padėčių konfigūraciją. Tuo tarpu greičiausio nusileidimo metodas leidžia aptikti artimiausią sąveikos energijos minimumą atitinkančią stabiliąkonfigūraciją. Daugeliu atvejų tokių konfigūracijų randame keletą ir žemiausios energijos konfigūracija (pagrindinė sistemos būsena) dažnai nėra labiausiai tikėtina. Siekiant kiekybiškai įvertinti sistemos struktūros neapibrėžtumą, atsirandantį dėl keleto konkuruojančių konfigūracijų buvimo, įvedama konfigūracinės entropijos sąvoka.

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