论文标题
退化漂移的亚稳定扩散
Metastable diffusions with degenerate drifts
论文作者
论文摘要
我们研究了与平滑函数$ f $相关的半经典witten laplacian $Δ_{f} $的光谱。我们假设$ f $是一个限制的摩尔斯 - 少特功能。在此假设下，我们表明$δ_{f} $允许与频谱的其余部分分开指数的小特征值。此外，我们为这些特征值建立眼环公式。我们的方法基于临界亚曼群附近的准例子的微局部构建体。
We study the spectrum of the semiclassical Witten Laplacian $Δ_{f}$ associated to a smooth function $f$ on ${\mathbb R}^d$. We assume that $f$ is a confining Morse--Bott function. Under this assumption we show that $Δ_{f}$ admits exponentially small eigenvalues separated from the rest of the spectrum. Moreover, we establish Eyring-Kramers formula for these eigenvalues. Our approach is based on microlocal constructions of quasimodes near the critical submanifolds.
