Statistical systems with nonintegrable interaction potentials

TL;DR

This paper introduces a new iterative method for analyzing statistical systems with nonintegrable interaction potentials, overcoming limitations of traditional mean-field approaches and applicable to both equilibrium and nonequilibrium systems.

Contribution

A novel iterative procedure is developed that systematically handles nonintegrable potentials, enabling accurate analysis beyond standard mean-field approximations.

Findings

The method effectively describes systems with hard-core and long-range potentials.

It allows for systematic derivation of higher-order corrections.

Applicable to both equilibrium and nonequilibrium statistical systems.

Abstract

Statistical systems composed of atoms interacting with each other trough nonintegrable interaction potentials are considered. Examples of these potentials are hard-core potentials and long-range potentials, for instance, the Lennard-Jones and dipolar potentials. The treatment of such potentials is known to confront several problems, e.g., the impossibility of using the standard mean-field approximations, such as Hartree and Hartree-Fock approximations, the impossibility of directly introducing coherent states, the difficulty in breaking the global gauge symmetry, which is required for describing Bose-Einstein condensed and superfluid systems, the absence of a correctly defined Fourier transform, which hampers the description of uniform matter as well as the use of local-density approximation for nonuniform systems. A novel iterative procedure for describing such systems is developed, starting from a correlated mean-field approximation, allowing for a systematic derivation of higher orders, and meeting no problems listed above. The procedure is applicable to arbitrary systems, whether equilibrium or nonequilibrium. The specification for equilibrium systems is presented. The method of extrapolating the expressions for observable quantities from weak coupling to strong coupling is described.