Charge and Current Sum Rules in Quantum Media Coupled to Radiation

TL;DR

This paper derives and tests sum rules for charge and current density correlations in quantum media coupled to radiation, revealing differences from microscopic Coulomb models and providing a unified framework using Rytov's fluctuational electrodynamics.

Contribution

It introduces a method to derive static and dynamic sum rules for charge and current correlations in quantum media with radiation coupling, including quantum and classical parts.

Findings

Sum rules fix moments of correlation functions in quantum media.

Current-current correlation function is integrable in space, unlike in microscopic models.

Classical and quantum parts of sum rules are explicitly separated.

Abstract

This paper concerns the equilibrium bulk charge and current density correlation functions in quantum media, conductors and dielectrics, fully coupled to the radiation (the retarded regime). A sequence of static and time-dependent sum rules, which fix the values of certain moments of the charge and current density correlation functions, is obtained by using Rytov's fluctuational electrodynamics. A technique is developed to extract the classical and purely quantum-mechanical parts of these sum rules. The sum rules are critically tested in the classical limit and on the jellium model. A comparison is made with microscopic approaches to systems of particles interacting through Coulomb forces only (the non-retarded regime). In contrast with microscopic results, the current-current correlation function is found to be integrable in space, in both classical and quantum regimes.