Sum Rules and Bose-Einstein Condensation

TL;DR

This paper discusses sum rules related to density and particle excitations in Bose-Einstein condensates, highlighting their implications on particle fluctuations, excitation structure, and a zero-temperature generalization of the Hohenberg-Mermin-Wagner theorem.

Contribution

It introduces sum rules that explicitly incorporate Bose-Einstein condensation effects, providing new insights into excitation behavior and fluctuations at zero temperature.

Findings

Sum rules reveal the coupling between density and particle excitations.

Generalization of the Hohenberg-Mermin-Wagner theorem at zero temperature.

Implications for fluctuations and elementary excitations in Bose-Einstein condensates.

Abstract

Various sum rules accounting for the coupling between density and particle excitations and emphasizing in an explicit way the role of the Bose-Einstein condensation are discussed. Important consequences on the fluctuations of the particle operator as well as on the structure of elementary excitations are reviewed. These include a recent generalization of the Hohenberg-Mermin-Wagner theorem holding at zero temperature. (To appear in "Bose-Einstein Condensation", A.Griffin, D.Snoke and S.Stringari eds., Cambridge Univ. Press)