Linking Scalar Elastodynamics and Non-Hermitian Quantum Mechanics

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 Schrödinger 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. arXiv:1910.07306v2 [cond-mat.soft]

Observation of vector solitary waves in soft laminates using a finite volume method

“…In the first test, we consider one layer bounded between two semi-infinite layers with different parameters, and note that these layers respond nonlinearly to finite-amplitude deformations. We subject the middle layer to an initial smallamplitude shear strain and show that the numerical solution captures the response as predicted by the analytical solution of the limiting linear problem (Shmuel and Moiseyev, 2020). The second test is of nonlinear waves and hence more challenging, where we address the canonical problem of wave scattering at an interface between two nonlinearly elastic half-spaces; here, however, the waves are of finite-amplitude and the displacements are coupled.…”

“…Note that ǫ 1 remains zero everywhere as it should in this uncoupled linear limit. The resultant waves are compared with the analytical solution for their length and velocity, see, e.g., the derivation by Shmuel and Moiseyev (2020). We first present in panel (b) the location of each strain local peak in the domain X 1 > 0.05 as function of time.…”

Chiral mode transfer of symmetry-broken states in anti-parity-time-symmetric mechanical system

“…A variety of intriguing properties have been found at EPs [6][7][8][9][10], which provide new schemes for controlling waves using balanced gain and loss. Based on the linkage between non-Hermitian quantum-mechanical and classical wave systems, the EP phenomenon associated with PT symmetry has been rapidly extended to acoustic [11][12][13] and elastodynamic realms [14][15][16][17]. Anomalous wave transport properties induced by EPs, such as asymmetric wave scattering [14,18,19], unidirectional sound focusing [13] and enhanced sensitivity [16,17], have been revealed.…”

“…Based on the linkage between non-Hermitian quantum-mechanical and classical wave systems, the EP phenomenon associated with PT symmetry has been rapidly extended to acoustic [11][12][13] and elastodynamic realms [14][15][16][17]. Anomalous wave transport properties induced by EPs, such as asymmetric wave scattering [14,18,19], unidirectional sound focusing [13] and enhanced sensitivity [16,17], have been revealed. Another topic of particular interest relates to the eigenvalue topological structure and unique mode-switching manipulation around an EP.…”

Non-Hermitian gap closure and delocalization in interacting directed polymers

“…For example, when non-Hermitian systems are periodic in space, their excitations are described by complex-valued band structures [17] which support uniquely non-Hermitian properties such as exceptional points (branch points) [18]. The physical implications of non-Hermitian band effects have been explored in a wide range of systems [19][20][21][22][23].…”