Abstract
Based on a statistical approach we describe the possible formation of a spatiallyinhomogeneous distribution in the system of interacting Fermi particles by long-rangeforces, and we demonstrate the nonperturbative calculation of the partitionfunction in this case. It is shown that particles interacting with an attractive1/r potential form clusters when the pressure due to the interactions balances the effectiverepulsion due to the Fermi statistics. A cluster is the equilibrium structure if we supposethat the average energy of interaction of two particles is much less than their averagekinetic energy. The dynamics of cluster formation is considered in this approach and thetime of relaxation to the equilibrium state is found. It is shown that phase transition froma spatially inhomogeneous state to a homogeneous state only occurs in a finite system. Thetemperature of such a phase transition is determined by the size of the finite system andthe average density.
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