Collective excitations and thermodynamics of disordered state: new insights into an old problem

Disorder has been long considered as a formidable foe of theoretical physicists in their attempts to understand systems' behavior. Here, we review recently accumulated data and propose that, from the point of view of calculating thermodynamic properties, the problem of disorder may not be as severe as has been hitherto assumed. We particularly emphasize that, contrary to the long-held view, collective excitations do not decay in disordered systems. We subsequently discuss recent experimental, theoretical, and modeling results related to collective excitations in disordered media, and show how these results pave the way to understanding thermodynamics of disordered systems: glasses, liquids, supercritical fluids, and spin glasses. An interesting insight from the recent work is the realization that most important changes of thermodynamic properties of the disordered system are governed only by its fundamental length, the interatomic separation. We discuss how the proposed theory relates to the previous approaches based on a general many-body statistical mechanics framework.