Discrete-to-continuum convergence of the density of states for Mathieu's equation
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912761702776832 |
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| author | Hofhansel, Peter Watson, Alexander B. |
| author_facet | Hofhansel, Peter Watson, Alexander B. |
| contents | The density of states of a self-adjoint operator generalizes the eigenvalue distribution of a Hermitian matrix. We prove convergence of the density of states for a tight-binding model with a slowly-varying periodic potential to the density of states of its continuum approximation, a Mathieu-type equation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_12039 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Discrete-to-continuum convergence of the density of states for Mathieu's equation Hofhansel, Peter Watson, Alexander B. Numerical Analysis Mathematical Physics Analysis of PDEs Spectral Theory The density of states of a self-adjoint operator generalizes the eigenvalue distribution of a Hermitian matrix. We prove convergence of the density of states for a tight-binding model with a slowly-varying periodic potential to the density of states of its continuum approximation, a Mathieu-type equation. |
| title | Discrete-to-continuum convergence of the density of states for Mathieu's equation |
| topic | Numerical Analysis Mathematical Physics Analysis of PDEs Spectral Theory |
| url | https://arxiv.org/abs/2512.12039 |