Dynamics and topology of non-Hermitian elastic lattices with non-local feedback control interactions

We investigate non-Hermitian elastic lattices characterized by non-local feedback interactions. In one-dimensional lattices, proportional feedback produces non-reciprocity associated with complex dispersion relations characterized by gain and loss in opposite propagation directions. For non-local co...

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Bibliographic Details
Published in:New journal of physics 2020-05, Vol.22 (5), p.53004
Main Authors: Rosa, Matheus I N, Ruzzene, Massimo
Format: Article
Language:English
Subjects:
Elastic properties
Feedback control
Frequencies
Investigations
Lattices
meta materials
non-Hermitian systems
non-reciprocal wave propagation
Physics
Reciprocation
Reciprocity
Skin effect
topological modes
Topology
Wave amplification
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Summary:We investigate non-Hermitian elastic lattices characterized by non-local feedback interactions. In one-dimensional lattices, proportional feedback produces non-reciprocity associated with complex dispersion relations characterized by gain and loss in opposite propagation directions. For non-local controls, such non-reciprocity occurs over multiple frequency bands characterized by opposite non-reciprocal behavior. The dispersion topology is investigated with focus on winding numbers and non-Hermitian skin effect, which manifests itself through bulk modes localized at the boundaries of finite lattices. In two-dimensional lattices, non-reciprocity is associated with directional wave amplification. Moreover, the combination of skin effect in two directions produces modes that are localized at the corners of finite two-dimensional lattices. Our results describe fundamental properties of non-Hermitian elastic lattices, and suggest new possibilities for the design of meta materials with novel functionalities related to selective wave filtering, amplification and localization. The considered non-local lattices also provide a platform for the investigation of topological phases of non-Hermitian systems.
ISSN:1367-2630
1367-2630
DOI:10.1088/1367-2630/ab81b6