Non-perturbative solutions of hierarchies of evolution equations for colliding particles

TL;DR

This paper develops a non-perturbative method using cluster expansions to construct solutions for hierarchies of evolution equations describing many colliding particles, advancing the mathematical understanding of such systems.

Contribution

It introduces a novel approach employing cluster expansions to solve hierarchies of evolution equations for many-particle systems non-perturbatively.

Findings

Constructed solutions to the BBGKY hierarchy using cluster expansions.

Established generating operators for solutions of the hierarchy.

Provided a framework for solving evolution equations for colliding particles.

Abstract

The article deals with the challenge of the construction of solutions to hierarchies of fundamental evolution equations for many colliding particles. The method of cluster expansions of the groups of operators of the Liouville equations for observables and a state is used to establish the generating operators of expansions representing solutions of the Cauchy problems of the BBGKY hierarchy (Bogolyubov-Born-Green-Kirkwood-Yvon) as well as of the dual BBGKY hierarchy, respectively.