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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2603.20834 |
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| _version_ | 1866911565285949440 |
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| author | Liang, Zhenguo Zhao, Zhiyan |
| author_facet | Liang, Zhenguo Zhao, Zhiyan |
| contents | We introduce the concept of {\it generalized reducibility}, which provides a flexible framework for analyzing the long-time behavior of solutions to quadratic quantum Hamiltonians. As an application of this notion, for many prescribed sub-exponential growth rates $f(t)$, either monotone or oscillatory, we explicitly construct time-decaying perturbations of the one-dimensional quantum harmonic oscillator such that the Sobolev norms of solutions grow at the rate $f(t)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_20834 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Generalized Reducibility and Growth of Sobolev Norms Liang, Zhenguo Zhao, Zhiyan Analysis of PDEs Dynamical Systems We introduce the concept of {\it generalized reducibility}, which provides a flexible framework for analyzing the long-time behavior of solutions to quadratic quantum Hamiltonians. As an application of this notion, for many prescribed sub-exponential growth rates $f(t)$, either monotone or oscillatory, we explicitly construct time-decaying perturbations of the one-dimensional quantum harmonic oscillator such that the Sobolev norms of solutions grow at the rate $f(t)$. |
| title | Generalized Reducibility and Growth of Sobolev Norms |
| topic | Analysis of PDEs Dynamical Systems |
| url | https://arxiv.org/abs/2603.20834 |