Abstract
The temporal modulation of a relevant parameter can be employed to induce modal transformations in Hermitian elastic lattices. When this is combined with a proper excitation mechanism, it allows to drive the energy transfer across the lattice with tunable propagation rates. Such a modal transformation, however, is limited by the adiabaticity of the process, which dictates an upper bound for the modulation speed. In this manuscript, we employ a non-Hermitian shortcut by way of a tailored gain and loss to violate the adiabatic limit and, therefore, to achieve superfast modal transformations. A quantitative condition for adiabaticity is firstly derived and numerically verified for a pair of weakly coupled time-dependent mechanical oscillators, which can be interpreted in the light of modal interaction between crossing states. It is shown that for sufficiently slow time-modulation, the elastic energy can be transferred from one oscillator to the other. A non-Hermitian shortcut is later induced to break the modal coupling and, therefore, to speed-up the modal transformation. The strategy is then generalized to elastic lattices supporting topological edge states. We show that the requirements for a complete edge-to-edge energy transfer are lifted from the adiabatic limit toward higher modulation velocities, opening up new opportunities in the context of wave manipulation and control.
Highlights
The emergence of novel wave behaviors in physics has been lately accompanied by growing interest in the field of mechanics
Topical examples include analogies to the Quantum Hall effect (QH) [11,12,13], Quantum Spin Hall effect (QSH) [14,15,16], and Quantum Valley Hall effect (QVH) [17,18,19], which have been employed for the fabrication of scattering-immune waveguides with unprecedented energy transfer capabilities
A fast modulation leads to scattering of energy to bulk modes and frequency conversion, which is generally undesired for communication and energy transfer purposes and limits the applicability of pumping protocols to a family of slow transfer mechanisms [41, 45]
Summary
The emergence of novel wave behaviors in physics has been lately accompanied by growing interest in the field of mechanics. An emerging trend leverages temporal (active) modulations of elastic or physical parameters [27] to accomplish different tasks, such as nonreciprocity [28,29,30,31,32,33,34,35], parametric amplification [36], frequency conversion [37] and edge-toedge pumping [38,39,40,41,42,43,44] This great variety of behaviors can be systematically observed in the same structure when the relevant parameters are biased with a different modulation speed. Such a transition has been employed in recent studies for invisibility
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