Long-wavelength excitations and structure factor of liquid 4He at T>0.

Abstract

An exact formula relating second moment of the density relaxation spectrum and static structure factor of simple liquids at arbitrary temperatures is used to derive the long-wavelength excitation frequencies of a liquid at low (but finite) temperatures, thus generalizing Feynman's (T=0) result on quantum liquids. At very low temperatures anomalous dispersion is expected while a purely linear frequency-wave-number relationship is estimated to apply for q\ensuremath{\ll}2 \ensuremath{\surd}6 (${\mathit{k}}_{\mathit{B}}$T)/(\ensuremath{\Elzxh}c) only. The static structure factor is shown to have a classical and a quantum contribution determining its long-wavelength properties at high (near ${\mathit{T}}_{\mathit{c}}$) and low temperatures, respectively.