Tagungsband - DAGA 2024
Beitrag
Beyond classic symmetry: Latent symmetry in acoustic waveguide networks (no manuscript)
Zusammenfassung:
The symmetries of an acoustic system are key tools in both its design and the understanding of its behavior. The scattering response of a reflection-symmetric setup, for instance, share the setup's symmetry, and the eigenmodes have definite parity. On the other hand, it is common knowledge that an asymmetric system has neither of these two properties.In this talk, I show that this common viewpoint is incomplete. In particular, I present several examples of networks of acoustic waveguides which, though asymmetric, share the same traits as their reflection-symmetric brethren. On a technical level, this can be explained by the fact that these networks are latently symmetric. A latent symmetry is a novel type of symmetry which, in general, is not apparent from a geometric inspection of the system. Instead, it becomes visible after a suitable dimensional reduction: The so-called isospectral reduction, which is akin to an effective Hamiltonian.Besides promoting an interdisciplinary approach (latent symmetries originate in mathematical graph theory), this talk demonstrates that the isospectral reduction technique is a powerful tool for the design of acoustic setups. Moreover, on a pedagogical level, the presented results show that even very simple setups can feature unexpected results and provide valuable insights.