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arXiv · 2603.20834

Generalized Reducibility and Growth of Sobolev Norms

Zhenguo Liang·Zhiyan Zhao
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Abstract

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 $f(t)$.

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Zhenguo Liang, Zhiyan Zhao. 2026-03-21. Generalized Reducibility and Growth of Sobolev Norms. https://arxiv.org/abs/2603.20834

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