Collective dynamics in glasses and its relation to the low-temperature anomalies

We present a systematic analysis of the low-temperature properties of glasses. In a first step we derive the low-temperature Hamiltonian of Lennard-Jones (LJ) glasses by a combination of numerical and analytical methods from first principles. This enables us to calculate the density of tunneling states, the coupling between tunneling states and phonons (deformation potential), and the extrema of C(T)/T-3[C(T) specific heat] for LJ glasses as functions of the velocity of sound, the density, and the glass transition temperature. In a second step we directly apply these results to more general glasses. Comparing the predictions for the four low-temperature parameters with experiment for a variety of glasses allows us to judge the degree to which their quantitative values are dominated by the individual microscopic structure. The agreement is excellent for the extrema of the specific heat and reasonable for the density of tunneling states and the deformation potential. Furthermore, we show from scaling arguments that such an agreement cannot be found for the peak of the sound absorption. From our simulations we can correlate the different degree of universality of the low-temperature observables with the different spatial extension of the relevant low-temperature excitations. In agreement with intuition, distinct collective dynamics translates into a weak dependence on the microscopic structure.