Linking scalar elastodynamics and non-Hermitian quantum mechanics

TL;DR

This paper bridges elastodynamics and non-Hermitian quantum mechanics, enabling new analytical tools for elastic wave phenomena and designing elastic systems with exceptional degeneracies for advanced sensing applications.

Contribution

It establishes the equivalence between elastodynamics and quantum mechanics equations and applies non-Hermitian perturbation theory to elastic systems for wave control and sensing.

Findings

Identified conditions for elastodynamics and Schrödinger equation equivalence.

Applied non-Hermitian perturbation theory to elastic systems.

Designed elastic assemblies with degeneracies for enhanced mass sensing.

Abstract

Recent years have seen a fascinating pollination of ideas from quantum theories to elastodynamics---a theory that phenomenologically describes the time-dependent macroscopic response of materials. Here, we open route to transfer additional tools from non-Hermitian quantum mechanics. We begin by identifying the differences and similarities between the one-dimensional elastodynamics equation and the time-independent Schrodinger equation, and finding the condition under which the two are equivalent. Subsequently, we demonstrate the application of the non-Hermitian perturbation theory to determine the response of elastic systems; calculation of leaky modes and energy decay rate in heterogenous solids with open boundaries using a quantum mechanics approach; and construction of degeneracies in the spectrum of these assemblies. The latter result is of technological importance, as it introduces an approach to harness extraordinary wave phenomena associated with non-Hermitian degeneracies for practical devices, by designing them in simple elastic systems. As an example of such application, we demonstrate how an assembly of elastic slabs that is designed with two degenerate shear states according to our scheme, can be used for mass sensing with enhanced sensitivity by exploiting the unique topology near the exceptional point of degeneracy.