Kramers-Kronig Relations For The Dielectric Function And The Static Conductivity Of Coulomb Systems

TL;DR

This paper investigates the dielectric permittivity of Coulomb systems, demonstrating it satisfies Kramers-Kronig relations and linking singularities to static conductivity and long-time correlations.

Contribution

It establishes the mutual influence of dielectric permittivity singularities in Coulomb systems and connects these to static conductivity and time correlation tails.

Findings

Dielectric permittivity satisfies Kramers-Kronig relations.

Singularities are linked to finite static conductivity.

Long tails of time correlation functions are involved.

Abstract

The mutual influence of singularities of the dielectric permittivity e(q,w) in a Coulomb system in two limiting cases w tends to zero, q tends to zero, and opposite q tends to zero, w tends to zero is established. It is shown that the dielectric permittivity e(q,w) satisfies the Kramers-Kronig relations, which possesses the singularity due to a finite value of the static conductivity. This singularity is associated with the long "tails" of the time correlation functions.