Temperature Dependence of the Condensate Fraction in SuperfluidHe4

Abstract

A temperature-dependent expression for the condensate fraction $n_0$ for He II based on a model Hamiltonian for superfluids is presented. This gives roughly the same magnitude for $n_0$ as is observed. The model also suggests the following behavior as $T\to 0$ for the roton effective mass ${\mu }_r\mathrm{}\left(T\right)={\mu }_r\mathrm{}\left(0\right)\mathrm{}[1-(\frac{m_{\mathrm{He}}}{24{\hslash }^3\mathrm{cn}}\left){\left(k_{\mathrm{B}}T\right)}^2\right]$ and the roton minimum energy $\Delta \mathrm{}\left(T\right)=\Delta \mathrm{}\left(0\right)\mathrm{}[1-(\frac{m_{\mathrm{He}}}{24{\hslash }^3\mathrm{cn}}\left){\left(k_{\mathrm{B}}T\right)}^2\right]$.