Bounds for the phonon-roton dispersion in superfluid 4He

Abstract

The sum rule approach is used to derive upper bounds for the dispersion law ${\omega }_0(q)$ of the elementary excitations of a Bose superfluid. Bounds are explicitly calculated for the phonon-roton dispersion in superfluid ${}^4$He, both at equilibrium ($\rho =0.02186$ Å${}^{-3}$) and close to freezing ($\rho =0.02622$ Å${}^{-3}$). The bound ${\omega }_0(q)\le 2S(q)\mid \chi (q){\mid }^{-1}$, where $S(q)$ and $\chi (q)$ are the static structure factor and density response respectively, is calculated microscopically for several values of the wavevector $q$. The results provide a significant improvement with respect to the Feynman approximation ${\omega }_F(q)=q^2(2mS(q){)}^{-1}$. A further, stronger bound, requiring the additional knowledge of the current correlation function is also investigated. New results for the current correlation function are presented.

arXiv comment13 pages, REVTEX, 7 figures available upon request or at http://anubis.science.unitn.it/~dalfovo/papers/papers.html

References in corpus (1)

• Static Response Function for Longitudinal and Transverse Excitations in Superfluid Helium

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