Collective Excitations

Many condensed-matter systems exhibit collective excitation modes involving coherent oscillations of the medium. For instance classical liquids and gases support sound waves. On quite general grounds one expects a well-defined sound wave to exist for all wavelengths much greater than the typical particle spacing. These modes are hydrodynamical in the sense that during one period of oscillation, many collisions occur between particles thereby maintaining local quasi-equilibrium. The particular details of the molecular collisions are largely irrelevant so long as they maintain the local quasi-equilibrium. The restoring force for the oscillation is the local pressure change induced by the local density change, and to a good approximation, one can compute the local pressure vs. density relationship using equilibrium thermodynamics.