Surface Region of Superfluid Helium as an Inhomogeneous Bose-Condensed Gas

TL;DR

The paper argues that the surface region of superfluid helium can be modeled as an inhomogeneous dilute Bose gas with nearly complete Bose-Einstein condensation, supported by numerical and theoretical analysis.

Contribution

It introduces a rigorous treatment of the helium surface as an inhomogeneous Bose condensate using a generalized Gross-Pitaevskii equation.

Findings

Numerical evidence supports complete Bose-Einstein condensation at the helium surface.

The surface region can be described by a generalized Gross-Pitaevskii equation.

The approach provides a rigorous theoretical framework for the surface Bose gas.

Abstract

We present arguments that the low density surface region of self-bounded superfluid $^4$He systems is an inhomogeneous dilute Bose gas, with almost all of the atoms occupying the same single-particle state at $T = 0$. Numerical evidence for this complete Bose-Einstein condensation was first given by the many-body variational calculations of $^4$He droplets by Lewart, Pandharipande and Pieper in 1988. We show that the low density surface region can be treated rigorously using a generalized Gross-Pitaevskii equation for the Bose order parameter.