  We report thermal conductivity measurements of porous Vycor glass when it is
empty and when the pores are filled with helium between 0.06 and 0.5 K. The
filling of liquid 3He and liquid 4He inside the Vycor pores brings about
respectively two and three fold reduction of the thermal conductivity as
compared with empty Vycor. This dramatic reduction of thermal conductivity, not
seen with solid 3He and 4He in the pores, is the consequence of hydrodynamic
sound modes in liquid helium that greatly facilitate the quantum tunneling of
the two-level systems (TLS) in Vycor and enhance the scattering of the thermal
phonons in the silica network.
