Long-range correlations of the surface charge density between electrical media with flat and spherical interfaces

TL;DR

This paper investigates the long-range behavior of surface charge density correlations at interfaces between different media, using both classical and quantum approaches, for flat and spherical geometries.

Contribution

It extends previous static results to dynamic correlations and applies a combined microscopic and macroscopic method to spherical interfaces.

Findings

Derived asymptotic long-range correlation functions.

Reproduced classical static results using linear response and electrostatic images.

Extended analysis to spherical interfaces between media.

Abstract

We study the asymptotic long-range behavior of the time-dependent correlation function of the surface charge density induced on the interface between two media of distinct dielectric functions which are in thermal equilibrium with one another as well as with the radiated electromagnetic field. We start with a short review which summarizes the results obtained by using quantum and classical descriptions of media, in both non-retarded and retarded regimes of particle interactions. The classical static result for the flat interface is rederived by using a combination of the microscopic linear response theory and the macroscopic method of electrostatic image charges. The method is then applied to the case of a spherically shaped interface between media.