Anharmonic and quasi-localized vibrations in jammed solids—Modes for mechanical failure

Abstract

We compare the harmonic and anharmonic properties of the vibrational modes in\n3-dimensional jammed packings of frictionless spheres interacting via\nrepulsive, finite range potentials. A crossover frequency is apparent in the\ndensity of states, the diffusivity and the participation ratio of the modes. At\nthis frequency, which shifts to zero at the jamming threshold, the vibrational\nmodes have a very small participation ratio implying that the modes are\nquasi-localized. The most anharmonic modes occur at low frequency which is\nopposite to what is normally found in crystals. The lowest frequency modes have\nthe strongest response to the pressure and the lowest energy barriers to\nmechanical failure.\n