论文标题
非线性量子谐波振荡器的Birkhoff正常形式低规律性
Birkhoff normal form in low regularity for the nonlinear quantum harmonic oscillator
论文作者
论文摘要
如果在$ \ mathbb {r} $上的非线性量子谐波振荡器的小初始解决方案给出了，我们对它们在适应的Sobolev空间中的长期行为感兴趣。我们以$ v $为乘电势将线性部分扰动，以线性频率满足非共振条件的方式。更确切地说，我们证明，对于几乎所有潜力$ v $，溶液的低模式几乎都保存了很长时间。
Given small initial solutions of the nonlinear quantum harmonic oscillator on $\mathbb{R}$, we are interested in their long time behavior in the energy space which is an adapted Sobolev space. We perturbate the linear part by $V$ taken as multiplicative potentials, in a way that the linear frequencies satisfy a non-resonance condition. More precisely, we prove that for almost all potentials $V$, the low modes of the solution are almost preserved for very long times.
