  We investigate the high-frequency behavior of the density of vibrational
states in three-dimensional elasticity theory with spatially fluctuating
elastic moduli. At frequencies well above the mobility edge, instanton
solutions yield an exponentially decaying density of states. The instanton
solutions describe excitations, which become localized due to the
disorder-induced fluctuations, which lower the sound velocity in a finite
region compared to its average value. The exponentially decaying density of
states (known in electronic systems as the Lifshitz tail) is governed by the
statistics of a fluctuating-elasticity landscape, capable of trapping the
vibrational excitations.
