Slow dispersion in Floquet-Dirac Hamiltonians
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866908921783910400 |
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| author | Bloch, Anthony Sagiv, Amir Steinerberger, Stefan |
| author_facet | Bloch, Anthony Sagiv, Amir Steinerberger, Stefan |
| contents | We study dispersive decay for non-autonomous Hamiltonian systems. While the general theory for dispersion in such non-autonomous systems is largely open, it was shown \cite{kraisler2025time} that there exists a time-periodically forced one-dimensional Dirac equation with unusually slow dispersive decay rate of $t^{-1/5}$. It is to be expected that such behavior is not generic and requires a very particular forcing term; we provide a more general ansatz and systematic procedure to construct such an equation with a dispersive decay rate no faster than $t^{-1/10}$. Our limitations are purely algebraic and it stands to reason that arbitrarily slow decay, $t^{-\varepsilon}$ for every $\varepsilon > 0$, should be achievable. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2603_28715 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Slow dispersion in Floquet-Dirac Hamiltonians Bloch, Anthony Sagiv, Amir Steinerberger, Stefan Analysis of PDEs Mathematical Physics 35Q41, 81Q05 We study dispersive decay for non-autonomous Hamiltonian systems. While the general theory for dispersion in such non-autonomous systems is largely open, it was shown \cite{kraisler2025time} that there exists a time-periodically forced one-dimensional Dirac equation with unusually slow dispersive decay rate of $t^{-1/5}$. It is to be expected that such behavior is not generic and requires a very particular forcing term; we provide a more general ansatz and systematic procedure to construct such an equation with a dispersive decay rate no faster than $t^{-1/10}$. Our limitations are purely algebraic and it stands to reason that arbitrarily slow decay, $t^{-\varepsilon}$ for every $\varepsilon > 0$, should be achievable. |
| title | Slow dispersion in Floquet-Dirac Hamiltonians |
| topic | Analysis of PDEs Mathematical Physics 35Q41, 81Q05 |
| url | https://arxiv.org/abs/2603.28715 |