Coulomb systems at low density

TL;DR

This paper reviews the behavior of correlations in low-density Coulomb systems, contrasting classical exponential screening with quantum cases, and discusses mathematical techniques and theorems related to their asymptotic properties.

Contribution

It provides a comprehensive review of classical and quantum Coulomb systems, introduces new combinatoric formulas for Mayer expansions, and discusses their implications for screening and molecular existence.

Findings

Classical Coulomb systems exhibit exponential decay of correlations (Debye-Hückel screening).

Quantum Coulomb systems likely lack exponential screening, with detailed asymptotic analysis provided.

New combinatoric formulas aid in understanding Mayer expansion coefficients and screening proofs.

Abstract

Results on the correlations of low density classical and quantum Coulomb systems at equilibrium in three dimensions are reviewed. The exponential decay of particle correlations in the classical Coulomb system -- Debye-H\"uckel screening -- is compared and contrasted with the quantum case where strong arguments are presented for the absence of exponential screening. Results and techniques for detailed calculations that determine the asymptotic decay of correlations for quantum systems are discussed. Theorems on the existence of molecules in the Saha regime are reviewed. Finally, new combinatoric formulas for the coefficients of Mayer expansions are presented and their role in proofs of results on Debye-H\"uckel screening is discussed.