论文标题
恒定级磁场的半经典Birkhoff正常形式
A semiclassical Birkhoff normal form for constant-rank magnetic fields
论文作者
论文摘要
我们考虑了Riemannian歧管上的半经典磁拉曲线$ \ MATHCAL {L} _H $，带有恒定且非散热磁场$ B $。在本地化假设是$ b $接受独特且非分类良好的假设下，我们在半经典限制$ \ hbar \ rightarrow 0 $中构建了三种连续的birkhoff普通形式，以描述$ \ nathcal {l} _h $的频谱。我们以$ \ hbar^{1/2} $的功率推断出所有特征值的扩展。
We consider the semiclassical magnetic Laplacian $\mathcal{L}_h$ on a Riemannian manifold, with a constant-rank and non-vanishing magnetic field $B$. Under the localization assumption that $B$ admits a unique and non-degenerate well, we construct three successive Birkhoff normal forms to describe the spectrum of $\mathcal{L}_h$ in the semiclassical limit $\hbar \rightarrow 0$. We deduce an expansion of all the eigenvalues under a threshold, in powers of $\hbar^{1/2}$.
