Cluster formation in the system of interacting Bose particles

Abstract

Based on statistical approach we described possible formation of spatially inhomogeneous distribution in the system of interacting Bose particles. The condition of cluster formation in both gas and condensed phases was obtained in this system. We studied the dynamics of cluster formation in the limit case of high temperatures. We compared the cluster-formation processes in the attractive system (with short-range interaction) and in the gravitational system at the low temperatures of Bose-Einstein condensate regime.

Self-gravitational system. New approach

“…One of them is the action of a collapsed gas equation (14) and the other one is the action corresponding to a spatially homogeneous distribution. In the case of collapses the action equation (14) is smaller than the action of spatially homogeneous distribution [5] (absolute minimum) and they are equal in the point of the collapse:…”

“…The formation of the spatial inhomogeneous distribution of the particle and field distribution which accompanies the gravitational interaction requires another approach which can describe the cluster formation which is related as collapsing states. In this paper the developed approach [3][4][5] suggests a statistical description of gravitational interacting particles of the system with regard to cluster formation. Systems with spatially inhomogeneous particle distributions are described in terms of various approaches.…”

“…Using the results of the hard sphere model we get an expression for action, for Boltzman statistics, that [4,5]:…”

“…Systems with spatially inhomogeneous particle distributions are described in terms of various approaches. Within this approach, special methods [3][4][5] have been proposed concerning the selection of states with thermodynamically stable spatially inhomogeneous particle distributions. When describing a wide range of systems of interacting particles with regard to the type of statistics but neglecting the quantum correlations, so that the interaction is treated in the classical manner, we can write the Hamiltonian of the system as given by [2,3,10,12] …”

“…Minimizing equation (15) by the size of cluster d = D/r m we obtain the optimum radius of the cluster [5]:…”