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arXiv · 2104.12778

Topology in non-linear mechanical systems

Po-Wei Lo·Krishanu Roychowdhury·Bryan Gin-ge Chen·Christian D. Santangelo·Chao-Ming Jian·Michael J. Lawler
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Abstract

Many advancements have been made in the field of topological mechanics. The majority of the works, however, concerns the topological invariant in a linear theory. We, in this work, present a generic prescription of defining topological indices which accommodates non-linear effects in mechanical systems without taking any approximation. Invoking the tools of differential geometry, a Z-valued quantity in terms of the Poincare-Hopf index, that features the topological invariant of non-linear zero modes (ZMs), is predicted. We further identify one type of topologically protected solitons that are robust to disorders. Our prescription constitutes a new direction of searching for novel topologically protected non-linear ZMs in the future.

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Po-Wei Lo, Krishanu Roychowdhury, Bryan Gin-ge Chen, Christian D. Santangelo, Chao-Ming Jian, Michael J. Lawler. 2021-04-26. Topology in non-linear mechanical systems. https://doi.org/10.1103/physrevlett.127.076802

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