论文标题
在相位循环上的半经典井的均匀光谱渐近级
Uniform spectral asymptotics for semiclassical wells on phase space loops
论文作者
论文摘要
我们考虑了半经典的自动化操作员，其符号在二维符号歧管上定义，在封闭曲线上达到了非分级最小$ B_0 $。我们得出了一种经典和量子的正常形式，除了系统的完整能力外，还可以在窗口$（ - \ infty，b_0+ε] $中获得特征值渐近肌，$ε> 0 $独立于半经典参数。这些渐近型在两个互补的环境中都可以在两个互补的环境中获得：策展人的策略是策略，而策展人是一个策划的策略。让人联想到Helffer-Sjöstrand的“ Miniwell”情况。
We consider semiclassical self-adjoint operators whose symbol, defined on a two-dimensional symplectic manifold, reaches a non-degenerate minimum $b_0$ on a closed curve. We derive a classical and quantum normal form which allows us, in addition to the complete integrability of the system, to obtain eigenvalue asymptotics in a window $(-\infty,b_0+ε]$ for $ε> 0$ independent on the semiclassical parameter. These asymptotics are obtained in two complementary settings: either a symmetry of the system under translation along the curve, or a Morse hypothesis reminiscent of Helffer-Sjöstrand's "miniwell" situation.
