  We study a disordered quantum solid incorporating two-level systems in which
a group of atoms (or a single atom) can experience coherent tunnelling between
two different positions and demonstrate that an effective mass deficit induced
by the presence of such objects can manifest itself only at relatively high
frequencies and should vanish in the low-frequency limit. The crossover to the
regime which can be associated with the appearance of an effective mass deficit
has been observed in recent torsional oscillator experiments.
