Modeling of spatial patterns formed by unstable particles on discrete grids by Monte Carlo method

I. Yu. Goliney

Institute for nuclear research of NAS of Ukraine, Kyiv, Ukraine 

Various spatial structures arise in systems of particles with finite lifetime in the conditions of constant generation due to the attraction [1-3]. The diffusion and aggregation of particles were modeled in a two-dimensional system by Monte Carlo method. The simulation was performed on a square and a hexagonal gratings. In the model, only one particle can occupy the lattice node. It can decay with a certain probability, can appear as a result of the generation and can move to the neighboring node. Interaction between particles was taken into account in the approach of the nearest neighbors. Modeling parameters were the intensity of generation, decay time and temperature.
The results showed that, unlike for the system of stable particles, the separation into two bulk phases does not occur. Instead, in a hexagonal grating's system at low temperatures and low densities, particles are gathered into small clusters, the size of which is determined by ratio of time required for a particle to move from one cluster to another and the lifetime. When the temperature rises, the clusters evaporate and the gas phase spreads to occupy the whole available volume. At high densities, the condensed phase occupies most of the volume with gaseous cavities inside. Generally, clusters or cavities are arranged in patterns resembling periodical, but the perfect superlattice is not formed due to the small particle lifetime as compared to the very slow overall cluster movement. The shape of the clusters is irregular. At medium densities clusters and cavities form a complex network.
The picture for the square grid is very different. Instead of roughly round clusters, diagonal strips of the condensed phase are formed. Such a difference is due to the fact that the mobility of particles at the ends of the strips is very slow. The particle move only by first jumping out of the cluster of the condensed gas, whereas on the hexagonal grating, the surface diffusion is not hampered.
Simulation was also carried out in the case of particle generation in a limited area. This does not change the general picture of the processes, but allows for different structures, for example, a condensed ring with a cavity in the center, condensed phase clusters arranged in a circle, and so on.
For a system of stable particles, the process of evaporation of the initial spherical island with thermalization of gas and the alignment of chemical potentials was studied. It was found that full alignment of chemical potentials occurs only at temperatures when the island is completely evaporated. Dependence of evaporation time on temperature is determined. At low temperatures, the time of evaporation becomes very high, and therefore the thermalization occurs only in the gas phase.

1.	L. V. Butov, A. C. Gossard, and D. S. Chemla, Nature 418, 751 (2002).
2.	M. Remeika, J. C. Graves, A. T. Hammark, A. D. Meyertholen, M. M. Fogler, L. V. Butov, M. Hanson, and A. C. Gossard, Phys. Rev. Lett. 102, 186803 (2009).
3.	A. A. Chernyuk and V. I. Sugakov, Phys. Rev. B 74, 085303 (2006). 

Моделювання просторових структур нестабільних частинок на  дискретній ґратці методом Монте-Карло
І. Ю. Голіней
Інститут ядерних досліджень НАН України, Київ, Україна

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