Classical behavior of strongly correlated electron systems of solids near a quantum critical point

► Collective excitations are studied in electron fluids near a quantum critical point (QCP). ► The QCP arises from violation of the stability condition for the Landau Fermi-liquid state. ► There exist phonon-like soft, weakly damped branches of transverse zero sound. ► Extremely low effective Debye temperatures drive electron transport to the classical regime.