Gap modes in Arnold tongues and their topological origins
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866913849904463872 |
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| author | Brown, Andrew Qin, Hong |
| author_facet | Brown, Andrew Qin, Hong |
| contents | Gap modes in a modified Mathieu equation, perturbed by a Dirac delta potential, are investigated. It is proved that the modified Mathieu equation admits stable isolated gap modes with topological origins in the unstable regions of the Mathieu equation, which are known as Arnold tongues. The modes may be identified as localized electron wavefunctions in a 1D chain or as toroidal Alfvén eigenmodes. A generalization of this argument shows that gap modes can be induced in regimes of instability by localized potential perturbations for a large class of periodic Hamiltonians. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2505_15007 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Gap modes in Arnold tongues and their topological origins Brown, Andrew Qin, Hong Mathematical Physics Other Condensed Matter Plasma Physics Gap modes in a modified Mathieu equation, perturbed by a Dirac delta potential, are investigated. It is proved that the modified Mathieu equation admits stable isolated gap modes with topological origins in the unstable regions of the Mathieu equation, which are known as Arnold tongues. The modes may be identified as localized electron wavefunctions in a 1D chain or as toroidal Alfvén eigenmodes. A generalization of this argument shows that gap modes can be induced in regimes of instability by localized potential perturbations for a large class of periodic Hamiltonians. |
| title | Gap modes in Arnold tongues and their topological origins |
| topic | Mathematical Physics Other Condensed Matter Plasma Physics |
| url | https://arxiv.org/abs/2505.15007 |