Quantum statistical effects in nano-oscillator arrays

We consider a large, free-standing array of coupled, planar oscillators each several hundred nanometers on a side fabricated from a single layer of dielectric. In particular, we predict the low-temperature heat capacity and Brillouin-scattered cross section based upon a numerical calculation of the density of states (DOS) for this nanostructured array. The DOS, which is interesting in its own right, is found to have an average value nearly independent of frequency and a number of gaps of varying depths. The predictions suggest that it should be possible to use low-temperature measurements of the Brillouin cross section and/or the specific heat to observe the quantum statistics obeyed by various rigid-body modes of the array, some of which involve the center-of-mass motion of a large number of atoms. As such, these measurements would result in a considerable extension of the domain in which quantum mechanics has been tested.