For about half a century, physicists have puzzled over vibrations in Glass at low temperatures. The reason: Glass carries sound waves and vibrations differently than other solids – it “vibrates differently.”
But what is the reason behind this? And how do we calculate the propagation of sound in Glass correctly?
Matthias Fuchs and Florian Vogel, two physicists from Konstanz, have recently discovered the answer by rewriting an old model developed roughly 20 years ago and rejected at the time by researchers.
A disordered solid is a glass. Glass is a solid whose constituent parts are not organized in a crystalline structure. The particles are almost flawlessly “lined up” in most solids, like building bricks arranged in a precise lattice. Such crystalline materials exhibit wavelike vibrations that are transmitted to their neighbors without damping when activated at low temperatures. Like a la-ola wave in a stadium, the vibration propagates as a constant wave without loss.
In Glass, the particles have random positions without stringent order. Hence, the oncoming oscillation waves are not carried on in a uniform pattern. Instead, the vibrations go ahead in a similarly random fashion and arrive at the particles’ arbitrary places. The homogeneous wave breaks as a result and splits into numerous smaller waves.
This dispersion effect brings on the damping. It is known as “Rayleigh damping” because physicist Lord Rayleigh used this mechanism of light scattering by atmospheric imperfections to explain why the sky looks blue.
About 20 years ago, physicists Marc Mezard, Giorgio Parisi, Anthony Zee, and colleagues proposed a model of oscillations in random positions known as the “Euclidean random matrix approach” (ERM), where they described the anomalies in Glass. However, due to some inconsistencies, the model was discarded by experts – and fell into oblivion.
Scientists in this study took up this old model again. They evaluated the new model by looking at its Feynman diagrams. They came up with answers to the unresolved issues that the scientific community at the time could not resolve. Richard Feynman introduced these helpful graphs in quantum field theory, which showed the regularities in the scattered wave patterns. Matthias Fuchs and Florian Vogel’s findings accurately estimated sound propagation and damping in Glass.
Matthias Fuchs, professor of soft condensed matter theory at the University of Konstanz, said, “Mezard, Parisi, and Zee were correct in their insightful model – harmonic oscillations in a disordered arrangement explain the anomalies of glass at low temperatures.”
“The re-discovered model, however, is far from the end of the story: For us, it’s the starting point: We have found the right model that we can now use for further calculations, especially of quantum mechanical effects.”
Journal Reference:
- Florian Vogel and Matthias Fuchs, Vibrational Phenomena in Glasses at Low Temperatures Captured by Field Theory of Disordered Harmonic Oscillators, Phys. Rev. Lett. 130, 236101 (2023). DOI: 10.1103/PhysRevLett.130.236101