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.
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