  We compare the harmonic and anharmonic properties of the vibrational modes in
3-dimensional jammed packings of frictionless spheres interacting via
repulsive, finite range potentials. A crossover frequency is apparent in the
density of states, the diffusivity and the participation ratio of the modes. At
this frequency, which shifts to zero at the jamming threshold, the vibrational
modes have a very small participation ratio implying that the modes are
quasi-localized. The most anharmonic modes occur at low frequency which is
opposite to what is normally found in crystals. The lowest frequency modes have
the strongest response to the pressure and the lowest energy barriers to
mechanical failure.
