Bounds for the phonon-roton dispersion in superfluid 4He

Details Bounds for the phonon-roton dispersion in superfluid 4He Bounds for the phonon-roton dispersion in superfluid 4He

1995-03-24

arxiv.org/abs/cond-mat/9503129v1

Physics

Condensed Matter

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

Scientific paper

10.1103/PhysRevB.52.1236

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 ($\rho=0.02186$ \AA$^{-3}$) and close to freezing ($\rho=0.02622$ \AA$^{-3}$). 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.

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