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We present an implementation of the analytical string theory recently appliedto the description of glasses. These are modeled as continuum media withembedded elastic string heterogeneities, randomly located and randomlyoriented, which oscillate around a straight equilibrium position with afundamental frequency depending on their length. The existence of a lengthdistribution reflects then in a distribution of oscillation frequencies whichis 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 anomaliesreported at frequencies comparable with the Boson Peak. Here we start from thegeneralized hydrodynamics to determine the dynamic correlation function$S(k,\omega)$ associated with the coherent, dispersive and attenuated, soundwaves resulting from a sound-string interference. Once the vibrational densityof states has been measured, we can use it for univocally fixing the stringlength distribution inherent to a given glass. The density-density correlationfunction obtained using such distribution is strongly constrained, and able toaccount for the experimental data collected on two prototypical glasses:glycerol and silica. The obtained string length distribution is compatible withthe typical size of elastic heterogeneities previously reported for silica andsupercooled liquids, and the atomic motion associated to the string dynamics isconsistent with the soft modes recently identified in large scale numericalsimulations as non-phonon modes responsible for the Boson Peak. The theory isthus in agreement with the most recent advances in the understanding of theglass specific dynamics and offers an appealing simple understanding of themicroscopic origin of the latter, while raising new questions on theuniversality or material-specificity of the string distribution properties.

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