The Surface Region of Superfluid $^4$He as a Dilute Bose-Condensed Gas

A. Griffin; S. Stringari

doi:10.1007/bf02569566

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arXiv · cond-mat/9606067

The Surface Region of Superfluid $^4$He as a Dilute Bose-Condensed Gas

A. Griffin·S. Stringari

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Abstract

In the low-density surface region of superfluid $^4$He, the atoms are far apart and collisions can be ignored. The only effect of the interactions is from the long-range attractive Hartree potential produced by the distant high-density bulk liquid. As a result, at $T=0$, all the atoms occupy the same single-particle state in the low-density tail. Striking numerical evidence for this 100\% surface BEC was given by Pandharipande and coworkers in 1988. We derive a generalized Gross-Pitaevskii equation for the inhomogeneous condensate wave function $Φ(z)$ in the low-density region valid at all temperatures. The overall amplitude of $Φ(z)$ is fixed by the bulk liquid, which ensures that it vanishes everywhere at the bulk transition temperature.

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A. Griffin, S. Stringari. 1996-06-10. The Surface Region of Superfluid $^4$He as a Dilute Bose-Condensed Gas. https://doi.org/10.1007/bf02569566

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