  We have theoretically predicted the density of states(DOS), the low
temperature specific heat, and Brillouin scattering spectra of a large, free
standing array of coupled nano-oscillators. We have found significant gaps in
the DOS of 2D elastic systems, and predict the average DOS to be nearly
independent of frequency over a broad band f < 50GHz. At low temperatures, the
measurements probe the quantum statistics obeyed by rigid body modes of the
array and, thus, could be used to verify the quantization of the associated
energy levels. These states, in turn, involve center-of mass motion of large
numbers of atoms, N > 1.e14, and therefore such observations would extend the
domain in which quantum mechanics has been experimentally tested. We have found
the required measurement capability to carry out this investigation to be
within reach of current technology.
