Bounds for the phonon-roton dispersion in superfluid 4He

J. Boronat; J. Casulleras; F. Dalfovo; S. Moroni; S. Stringari

doi:10.1103/physrevb.52.1236

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Bounds for the phonon-roton dispersion in superfluid 4He

J. Boronat·J. Casulleras·F. Dalfovo·S. Moroni·S. Stringari

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Abstract

The sum rule approach is used to derive upper bounds for the dispersion law $ω_0(q)$ of the elementary excitations of a Bose superfluid. Bounds are explicitly calculated for the phonon-roton dispersion in superfluid $^4$He, both at equilibrium ($ρ=0.02186$ Å$^{-3}$) and close to freezing ($ρ=0.02622$ Å$^{-3}$). The bound $ω_0(q) \le 2S(q)\midχ(q)\mid^{-1}$, where $S(q)$ and $χ(q)$ 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 $ω_F(q)= q^2(2mS(q))^{-1}$. 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.

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J. Boronat, J. Casulleras, F. Dalfovo, S. Moroni, S. Stringari. 1995-03-24. Bounds for the phonon-roton dispersion in superfluid 4He. https://doi.org/10.1103/physrevb.52.1236

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