Liquid helium in disorder and boson localization

Neutron scattering measurements of the excitations of liquid $^4$He confined in three porous media focusing on temperatures around the superfluid-normal fluid critical temperature $T_c$ are presented and discussed. The three porous media are Vycor ($T_c = 2.05$ K at SVP), 44 {\AA} pore diameter gelsil ($T_c = 1.92$ K at SVP) and 25 {\AA} pore diameter gelsil ($T_c \approx 1.0$ K at SVP)~${^{[1,2]}}$. In all these media, liquid $^4$He supports well-defined phonon-roton excitations above $T_c$, in the "normal" phase (up $T_\lambda = 2.17$ K at SVP). Since well-defined excitations are associated with Bose-Einstein condensation (BEC), this suggests that there is BEC in the "normal" phase. Also, since there is no superflow, this BEC is apparently localized in the media separated by regions of normal fluid. In this picture, the superfluid-normal transition in disorder is associated with an extended-localized BEC crossover with localized BEC remaining above $T_c$~${^{[3]}}$. \\${^{[1]}}$F. Albergamo et al., Phys. Rev. B 69, 014514 (2004) \\${^{[2]}}$J. V. Pearce et al., Phys. Rev. Lett. 93, 145303 (2004)) \\ ${^{[3]}}$H. R. Glyde et al., Phys. Rev. Lett. 84, 2646 (2000)