The strange behavior of sound through solids

You don’t have to see everything to believe it; certain things are easier to hear, like a train approaching its station. In a recent article published in Physical Verification LettersResearchers put their ears to the rail and discovered a new property of the scattering of amplitudes based on their study of sound waves through solid matter.

Whether light or sound, physicists look at the probability of particle interactions (yes, sound can behave like a particle) in terms of probability curves or scattering amplitudes. It is well known that when the momentum or energy of one of the scattered particles goes to zero, the scattering amplitudes should always scale with integer powers of the momentum (i.e. p¹p²p³, Etc.). However, what the research team found was that amplitude can be proportional to a fractional power (i.e. p^1/2p^1/3p^1/4Etc.).

Why is that important? While quantum field theories such as the Standard Model allow researchers to make predictions about particle interactions with extreme accuracy, it is still possible to improve on the current foundation of fundamental physics. When a new behavior is demonstrated – such as B. Fractional power scaling – scientists have the opportunity to reconsider or revise existing theories.

This work, carried out by Angelo Esposito (Institute for Advanced Study), Tomáš Brauner (University of Stavanger) and Riccardo Penco (Carnegie Mellon University), specifically considers the interactions of sound waves in solids. To illustrate this concept, imagine a block of wood with speakers attached to either end. As soon as the speakers are turned on, two sound waves – phonons – collide and scatter, similar to collisions in a particle accelerator. If a speaker is set to a certain limit such that the momentum of the phonon is zero, the resulting amplitude can be proportional to a fractional power. This scaling behavior, the team explains, is probably not limited to phonons in solids, and detecting it can help study scattering amplitudes in many different contexts, from particle physics to cosmology.

“The detailed properties of scattering amplitudes have recently been studied with much vigour,” Esposito said. “The goal of this broad program is to classify possible behavior patterns of scattering amplitudes, both to make some of our calculations more efficient, and more ambitious, to provide new foundations of quantum field theory.”

Feynman diagrams have long been an indispensable tool for particle physicists, but they have certain limitations. For example, high-precision calculations can require tens of thousands of Feynman diagrams to be entered into a computer to describe particle interactions. With a better understanding of scattering amplitudes, researchers may be able to more easily localize particle behavior rather than relying on the top-down approach of Feynman diagrams, improving the efficiency of calculations.

“The present work unveils a twist in history by showing that condensed matter physics has a much richer phenomenology of scattering amplitudes than what was previously seen in fundamental relativistic physics,” Esposito added. “The discovery of fractional scaling invites further work on scattering amplitudes of collective matter vibrations, with solids becoming the focus.”