Topological Dynamics of Synthetic Molecules
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866910703344943104 |
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| author | Zhu, Yuming Prodan, Emil |
| author_facet | Zhu, Yuming Prodan, Emil |
| contents | We study the dynamics of synthetic molecules whose architectures are generated by space transformations from a point group acting on seed resonators. We show that the dynamical matrix of any such molecule can be reproduced as the left regular representation of a self-adjoint element from the stabilized group's algebra. Furthermore, we use elements of representation theory and K-theory to rationalize the dynamical features supported by such synthetic molecules up to topological equivalences. These tools enable us to identify a set of fundamental models which generate by superposition all possible dynamical matrices up to homotopy equivalences. Interpolations between these fundamental models give rise to topological spectral flows. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2411_11638 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Topological Dynamics of Synthetic Molecules Zhu, Yuming Prodan, Emil Mathematical Physics Materials Science We study the dynamics of synthetic molecules whose architectures are generated by space transformations from a point group acting on seed resonators. We show that the dynamical matrix of any such molecule can be reproduced as the left regular representation of a self-adjoint element from the stabilized group's algebra. Furthermore, we use elements of representation theory and K-theory to rationalize the dynamical features supported by such synthetic molecules up to topological equivalences. These tools enable us to identify a set of fundamental models which generate by superposition all possible dynamical matrices up to homotopy equivalences. Interpolations between these fundamental models give rise to topological spectral flows. |
| title | Topological Dynamics of Synthetic Molecules |
| topic | Mathematical Physics Materials Science |
| url | https://arxiv.org/abs/2411.11638 |