Short-distance properties of Coulomb systems

TL;DR

This paper derives exact high-momentum behavior of Coulomb systems using operator product expansion, revealing quantum power-law tails in momentum distribution and structure factors that vanish classically.

Contribution

It provides the first exact derivation of the asymptotic momentum distribution and structure factor tails for Coulomb systems in any state or temperature.

Findings

Power-law tails in momentum distribution determined by contact pair distribution function

Quantum effects cause tails to vanish in the classical limit

Classical and high-temperature limits do not agree as shown by virial expansion

Abstract

We use the operator product expansion to derive exact results for the momentum distribution and the static structure factor at high momentum for a jellium model of electrons in both two and three dimensions. It is shown that independent of the precise state of the Coulomb system and for arbitrary temperatures, the asymptotic behavior is a power law in the momentum, whose strength is determined by the contact value of the pair distribution function $g(0)$. The power-law tails are quantum effects which vanish in the classical limit $\hbar \to 0$. A leading order virial expansion shows that the classical and the high-temperature limit do not agree.