Elastic anomalies in glasses: the string theory understanding in the case of Glycerol and Silica

We present an implementation of the analytical string theory recently applied to the description of glasses. These are modeled as continuum media with embedded elastic string heterogeneities, randomly located and randomly oriented, which oscillate around a straight equilibrium position with a fundamental frequency depending on their length. The existence of a length distribution reflects then in a distribution of oscillation frequencies which is responsible for the Boson Peak in the glass density of states. Previously, it has been shown that such a description can account for the elastic anomalies reported at frequencies comparable with the Boson Peak. Here we start from the generalized hydrodynamics to determine the dynamic correlation function $S(k,\omega)$ associated with the coherent, dispersive and attenuated, sound waves resulting from a sound-string interference. Once the vibrational density of states has been measured, we can use it for univocally fixing the string length distribution inherent to a given glass. The density-density correlation function obtained using such distribution is strongly constrained, and able to account for the experimental data collected on two prototypical glasses: glycerol and silica. The obtained string length distribution is compatible with the typical size of elastic heterogeneities previously reported for silica and supercooled liquids, and the atomic motion associated to the string dynamics is consistent with the soft modes recently identified in large scale numerical simulations as non-phonon modes responsible for the Boson Peak. The theory is thus in agreement with the most recent advances in the understanding of the glass specific dynamics and offers an appealing simple understanding of the microscopic origin of the latter, while raising new questions on the universality or material-specificity of the string distribution properties.Comment: 15 pages, 8 figure

Multiple scattering of elastic waves by pinned dislocation segments in a continuum

The coherent propagation of elastic waves in a solid filled with a random distribution of pinned dislocation segments is studied to all orders in perturbation theory. It is shown that, within the independent scattering approximation, the perturbation series that generates the mass operator is a geometric series that can thus be formally summed. A divergent quantity is shown to be renormalizable to zero at low frequencies. At higher frequencies said quantity can be expressed in terms of a cut-off with dimensions of length, related to the dislocation length, and physical quantities can be computed in terms of two parameters, to be determined by experiment. The approach used in this problem is compared and contrasted with the scattering of de Broglie waves by delta-function potentials as described by the Schr\"odinger equation

The scattering of phonons by infinitely long quantum dislocations segments and the generation of thermal transport anisotropy in a solid threaded by many parallel dislocations

A canonical quantization procedure is applied to the interaction of elastic waves --phonons-- with infinitely long dislocations that can oscillate about an equilibrium, straight line, configuration. The interaction is implemented through the well-known Peach-Koehler force. For small dislocation excursions away from the equilibrium position, the quantum theory can be solved to all orders in the coupling constant. We study in detail the quantum excitations of the dislocation line, and its interactions with phonons. The consequences for the drag on a dislocation caused by the phonon wind are pointed out. We compute the cross-section for phonons incident on the dislocation lines for an arbitrary angle of incidence. The consequences for thermal transport are explored, and we compare our results, involving a dynamic dislocation, with those of Klemens and Carruthers, involving a static dislocation. In our case, the relaxation time is inversely proportional to frequency, rather than directly proportional to frequency. As a consequence, the thermal transport anisotropy generated on a material by the presence of a highly-oriented array of dislocations is considerably more sensitive to the frequency of each propagating mode, and therefore, to the temperature of the material.Comment: 21 pages, 8 figure