Superfluid density of thin<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mmultiscripts><mml:mrow><mml:mi mathvariant="normal">He</mml:mi></mml:mrow><mml:mprescripts/><mml:mrow/><mml:mrow><mml:mn>4</mml:mn></mml:mrow><mml:mrow/><mml:mrow/></mml:mmultiscripts></mml:mrow></mml:math>films adsorbed in porous Vycor glass

We have studied the superfluid density of thin superfluid $^{4}\mathrm{He}$ films absorbed in porous Vycor glass. At low temperatures we have used a third-sound technique to examine the Landau elementary excitations. We observed phonons with a ${T}^{2}$ temperature dependence and rotons with a 5-K energy gap. At higher temperatures we have examined the superfluid density in the critical region. The superfluid density follows a power law similar to that of bulk $^{4}\mathrm{He}$ with an exponent at the bulk value. We conclude that these effects are due to the three-dimensional geometry of the substrate.

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