  We have studied the collective phenomena of multicomponent glasses at ultra
low temperatures [Strehlow, et. al, Phys. Rev. Lett 80, 5361 (1998)] by taking
into account the proper interaction between tunneling centers. We have
considered both double and triple well potentials with different types of
interactions. We show that a phase with coherent motion appears for a range of
parameters when the path of tunneling is coursed by an interaction of the XY
type, while the usual Ising like interaction does not lead to the expected
collective phenomena. In the phase of coherent motion, the dipole moment and
the low-energy levels oscillate with a frequency proportional to the number of
tunneling centers in the system. Simultaneous level crossing occurs between the
ground and first excited states. The effects of long-range interactions and
also of random couplings have been also studied for a one- and two-dimensional
array of tunneling centers. We find that long-range interactions do not affect
the coherent motion, while a wide distribution of random couplings destroys the
collective effects.
