Upper Bounds to the Ground State Energies of the One- and Two-Component Charged Bose Gases

TL;DR

This paper establishes upper bounds for the ground state energies of one- and two-component charged Bose gases, confirming long-standing asymptotic formulas and validating Bogolubov's pairing theory in these systems.

Contribution

It provides rigorous upper bounds that match the conjectured asymptotic formulas by Foldy and Dyson, confirming their validity for large particle numbers.

Findings

Upper bound for one-component gas matches Foldy's 1961 formula.

Upper bound for two-component gas matches Dyson's 1967 conjecture.

Results validate Bogolubov's pairing theory for these systems.

Abstract

We prove upper bounds on the ground state energies of the one- and two-component charged Bose gases. The upper bound for the one-component gas agrees with the high density asymptotic formula proposed by L. Foldy in 1961. The upper bound for the two-component gas agrees in the large particle number limit with the asymptotic formula conjectured by F. Dyson in 1967. Matching asymptotic lower bounds for these systems were proved in references \cite{LS} and \cite{LS2}. The formulas of Foldy and Dyson which are based on Bogolubov's pairing theory have thus been validated.