Particle Dynamics Driven by Charge Exchange

TL;DR

This paper develops and analyzes a mathematical model for particle dynamics driven by charge exchange, extending existing models to include densities on the entire integer lattice and exploring their stability and equilibria.

Contribution

The paper introduces a novel extension of the exchange-driven growth model to integer lattice densities and provides a comprehensive analysis of its well-posedness and equilibrium stability.

Findings

Established global well-posedness for the model.

Analyzed equilibrium structure under detailed balance.

Investigated stability using entropy methods.

Abstract

We introduce and analyse a mathematical model describing the dynamics of particles generated by charge-exchange interactions. The model extends the well-established exchange-driven growth model, previously studied in several works, by allowing for particle densities defined on the entire integer lattice. Despite the many similarities between the two models, substantial differences arise both in their qualitative behaviour and in their mathematical analysis. Under suitable assumptions on the kernel in the collision operator, we establish global well-posedness in the class of nonnegative densities with finite first moment. Moreover, under a detailed balance condition, we investigate the structure of equilibria and analyse their stability by means of entropy methods.