Cluster formation in the Fermi system with long-range interaction

TL;DR

This paper investigates how long-range attractive forces cause clustering in Fermi systems, providing a nonperturbative partition function calculation and analyzing cluster formation dynamics.

Contribution

It introduces a statistical method to describe inhomogeneous distributions and demonstrates cluster formation due to long-range interactions in Fermi systems.

Findings

Particles with attractive 1/r potential form stable clusters

Cluster formation occurs when interaction energy is much less than kinetic energy

The relaxation time to equilibrium was estimated

Abstract

Based on statistical approach we described possible formation of spatially inhomogeneous distribution in the system of interacting Fermi particles by long-rage forces, and we demonstrated nonperturbative calculation of the partition function in this case. It was shown, that particles interacting with an attractive $1/r$ potential form clusters. Cluster is equilibrium structure, if we suppose that average energy of interaction of two particles is much less than their average kinetic energy $kT$. The analogy between self-gravitation gas and plasma was shown. The dynamics of cluster formation was considered with help hydrodynamical and statistical approaches, and time of relaxation to equilibrium state was found.