Self-gravitational system. New approach

Abstract

The field theory approach to statistical description of the system of gravitational interacting particles is proposed in order to describe spatially inhomogeneous structures. A nonperturbutive calculation of the partition function is demonstrated for such a system. Spatially inhomogeneous system's state -cluster is considered. The spatial distribution function, cluster's size and the conditions of phase transition to the collapsed phase are determined exactly in this approach. : 23.23.+x, 56.65.Dy The statistical description of the of interacting particles has attracted a permanent attention. A few model systems of interacting particles are known, as far as the partition function can be exactly evaluated, at least, in the thermodynamic limit. The gravitation system does not have an exact solution so far. The problem of mean-field thermodynamics of self-gravitational system lies in the possible collapse in this system. An important point, which emerges from these studies and which is quite obvious is the non-extensiveness of the usual thermodynamic function in the thermodynamic limit, when the number of particle N → ∞. But the example of scaling consideration suggests an extensive homogeneous mean field in thermodynamic limit when the N → ∞ [1]. 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. 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] Key words: gravitational interaction, cluster, spatially inhomogeneous distribution, collapse, soliton solution PACSwhere ε s is the additive part of the particle energy in the state s which is equal to the kinetic energy in most cases, W ss are attraction energies for the particles in the states s and s . The macroscopic states of the system are described by a set of occupation numbers n s . Index s labels an individual particle state; it can also correspond to a fixed site of the Ising lattice [10], whose explicit form is irrelevant in the continuum approximation. This expression for the Hamiltonian also holds for the model of substitution and interstitial solid solutions with two atom species present [2]. It is clear that to calculate the partition function is a rather involved problem even in the case of the...

Cluster formation in a Fermi system with long-range attraction

“…In the papers [6,7] this approach was applied to the investigation of a system with long-range interacting Bose particles. It has been shown that the spatial distribution of such a system is inhomogeneous and is like a finite-size cluster.…”