Anomalous Sound Velocity and Dielectric Shift in Glass: a Renormalization Technique for Mechanical and Dielectric Susceptibilities from Generic Coupled Block Model


Abstract in English

Glass sound velocity shift was observed to be longarithmically temperature dependent in both relaxation and resonance regimes: $Delta c/c=mathcal{C}ln T$. It does not monotonically increase with temperature from $T=0$K, but to reach a maximum around a few Kelvin. Different from tunneling-two-level-system (TTLS) which gives the slope ratio between relaxation and resonance regimes $mathcal{C}^{rm rel }:mathcal{C}^{rm res }=-frac{1}{2}:1$, we develop a generic coupled block model to give $mathcal{C}^{rm rel }:mathcal{C}^{rm res }=-1:1$, which agrees well with the majority of experimental measurements. We use electric dipole-dipole interaction to carry out a similar behavior for glass dielectric constant shift $Delta epsilon/epsilon=mathcal{C}ln T$. The slope ratio between relaxation and resonance regimes is $mathcal{C}^{rm rel}:mathcal{C}^{rm res}=1:-1$ which agrees with dielectric measurements quite well. By developing a renormalization procedure for non-elastic stress-stress and dielectric susceptibilities, we prove these universalities essentially come from $1/r^3$ long range interactions, independent of materials microscopic properties.

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