In this talk I will present theoretical results of investigations of phonon dynamics on optomechanical platforms (periodical multi-element mechanical structures embedded in an optical cavity). Optomechanical arrays can be designed as reconfigurable platforms for engineering the coupling between multiple mechanical and electromagnetic modes; such a device operates in a regime where the array is transmissive and light permeates through the structure. This allows both for the enhancement of the optomechanical response and the coupling to specific collective motional modes of the array . Effective long-range phonon-phonon interactions can be achieved by addressing these transmissive modes.
Moreover, arising from structural resonances defined by the light fields, these interactions are naturally tunable and reconfigurable .
Two illustrations of controlled many-body dynamics made possible in this setting are provided: (i) In the bad-cavity regime of optomechanics, the structure acts as a beam-splitter array for phonons with effective long-range mode coupling, enabling the investigation of phononic random walks and controlled transfer of heat between distant elements in the array. (ii) In the good-cavity regime, coherent and reconfigurable transfer of single excitations is shown to be possible between distant array elements.
 /Strong coupling and long-range collective interactions in optomechanical arrays/, A. Xuereb, C. Genes and A. Dantan, Phys. Rev.
Lett. 109, 223601 (2012).**
 /Reconfigurable long-range phonon dynamics in optomechanical arrays/, A. Xuereb, C. Genes, G. Pupillo, M. Paternostro and A. Dantan,