Discrete grid Monte Carlo Modelling of spatial structures formed by unstable particles in nonequilibrium conditions 

Igor Goliney

Institute for Nuclear Research, National Academy  of Science, Ukraine

Systems of attracting finite-lifetime particles under condition of constant generation form a variety of spatial structures [1-3]. Such systems include, for example, indirect excitons created in double well   heterostructures under intense light illumination.
Diffusion and aggregation of particles has been modeled in 2D  by Monte Carlo method. Modeling has been performed on a square and a hexagonal grids. The model allows occupation of any grid site by a single particle. A particle may decay with a certain probability, may be generated  and may move to the neighbor site. Interparticle interaction was accounted for in the nearest neighbor approximation. Modeling parameters included the generation rate, the decay time and temperature.
Results showed that unlike for the system of stable particles formation of the two large regions of different phases does not occur.  Instead, in the system with hexagonal grid, at low temperature and low density the particles aggregate into small clusters, the size and spacing of which is determined by the time required for a particle to travel between the clusters as compared to the lifetime. At higher temperature the clusters evaporate and the gas phase occupies the whole volume. At large  density, the condensed phase occupies most of the simulation box volume but gas voids arise in this case. Generally the structure of the clusters or voids is close to the regular, but a perfect superlattice does not develop due the smallness of the lifetime in comparison to very slow motion of clusters. The shape of clusters is irregular. At the intermediate densities, the clusters and voids form complex networks.    
The situation has been significantly different for a square grid. Instead of approximately round clusters, the system has tended to the stripes of the condensed phase. The difference may be explained by the fact that the particles are immobilized at the kinks of the stripes. A particle  may move away from a kink only by jumping out of the condensed phase while for the hexagonal grade, there is no barrier for  the surface diffusion. 
Modeling was also performed for the cases of limited areas of generation.  This limitation does not affect the general picture but allows to obtain a number of  different structures, for example a ring of the condensed phase with a void in a center, clusters arranged into a ring formation etc. 
For a system of stable particles, the process of the evaporation of the initial round island has been studied with the effect of gas thermalization and the balancing of chemical potentials.  It was found that the complete equalization of chemical potential occurs only at temperatures when the island evaporates completely. The evaporation time dependence on temperature has been determined. At low temperature the evaporation time is too large, so the thermalization occurs only in the gas phase. 

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