Tagged particle process in continuum with singular interactions

TL;DR

This paper develops a mathematical framework using Dirichlet forms to model the movement of a single particle within an infinite interacting particle system, accommodating complex potentials including singular and long-range interactions.

Contribution

It introduces a novel construction method for tagged particle dynamics in infinite systems with singular, negative, and long-range potentials, expanding the scope of models that can be analyzed.

Findings

Successfully constructed dynamics for particles with Lennard-Jones type potentials.

Extended the applicability of Dirichlet form techniques to singular and infinite-range interactions.

Provided a rigorous mathematical foundation for studying tagged particles in complex environments.

Abstract

By using Dirichlet form techniques we construct the dynamics of a tagged particle in an infinite particle environment of interacting particles for a large class of interaction potentials. In particular, we can treat interaction potentials having a singularity at the origin, non-trivial negative part and infinite range, as e.g., the Lennard-Jones potential.