This research was inspired by the work of many scientists building resonator networks, which are systems with components that interact in complex ways, similar to the vibrations of a musical instrument. While analyzing nanoscale graphene resonators through scanning interference microscopy (SIM), Horowitz and the Alemán group encountered a puzzling result. The response curve from the resonators suggested only two peaks, implying two resonators. However, SIM images revealed a third resonator, challenging previous assumptions about how to interpret such data. This unexpected discovery led to the realization that the traditional spectrum of resonators provided misleading information about the true size of a network and raised questions about how to determine all the mechanical parameters of a resonator network.
In her presentation, Horowitz discussed three methods for determining all the mechanical parameters of a resonator network: dismantling the network, using curve-fitting techniques, or applying NetMAP, a new algebraic formalism. She discussed how she used simulations to validate the NetMAP approach, finding that successful application of NetMAP primarily depends on the signal-to-noise ratio—a crucial factor that determines the reliability of the results.
NetMAP offers new possibilities for analyzing complex resonator networks without having to disassemble them, providing a clearer understanding of their mechanical properties. Since a wide range of systems exhibit resonance, this new formalism may prove valuable for future studies in diverse fields including quantum computing, nanotechnology, engineering, neuroscience, and astrophysics.
