Linear Response for Confined Particles

TL;DR

This paper develops a linear response theory for charges in confined, nonuniform environments, deriving a kinetic framework to analyze fluctuations and force autocorrelations in such systems.

Contribution

It introduces an exact short-time linear Markov kinetic theory for nonuniform charge distributions in confining potentials.

Findings

Derived a linear response function for nonuniform charge densities.

Solved the kinetic equation using an effective mean field approach.

Discussed the autocorrelation function of the total force on charges.

Abstract

The dynamics of fluctuations is considered for electrons near a positive ion or for charges in a confining trap. The stationary nonuniform equilibrium densities are discussed and contrasted. The linear response function for small perturbations of this nonuniform state is calculated from a linear Markov kinetic theory whose generator for the dynamics is exact in the short time limit. The kinetic equation is solved in terms of an effective mean field single particle dynamics determined by the local density and dynamical screening by a dielectric function for the non-uniform system. The autocorrelation function for the total force on the charges is discussed.