论文标题
Schrödinger操作员对矢量捆绑的隧道效果
The Tunneling Effect for Schrödinger operators on a Vector Bundle
论文作者
论文摘要
In the semiclassical limit h to 0, we analyze a class of self-adjoint Schrödinger operators H_h = h^2 L + h W + V id_E acting on sections of a vector bundle E over an oriented Riemannian manifold M where L is a Laplace type operator, W is an endomorphism field and the potential energy V has non-degenerate minima at a finite number of points m_1, ... M_R中的M_R，称为潜在的井。我们使用M_J附近的WKB型的准膜来进行与H_H的低谎言特征值相关的特征功能，我们分析了隧道效应，即在低谎言特征值之间的分裂，例如。在某些对称配置中产生。从技术上讲，我们通过相互作用矩阵来处理不同潜在孔之间的耦合，我们考虑了连接两个潜在孔的单个最小的大地测量（相对于相关的agmon指标）的情况，并且是尺寸l + 1的最小测量的下层。
In the semiclassical limit h to 0, we analyze a class of self-adjoint Schrödinger operators H_h = h^2 L + h W + V id_E acting on sections of a vector bundle E over an oriented Riemannian manifold M where L is a Laplace type operator, W is an endomorphism field and the potential energy V has non-degenerate minima at a finite number of points m_1, ... m_r in M, called potential wells. Using quasimodes of WKB-type near m_j for eigenfunctions associated with the low lying eigenvalues of H_h, we analyze the tunneling effect, i.e. the splitting between low lying eigenvalues, which e.g. arises in certain symmetric configurations. Technically, we treat the coupling between different potential wells by an interaction matrix and we consider the case of a single minimal geodesic (with respect to the associated Agmon metric) connecting two potential wells and the case of a submanifold of minimal geodesics of dimension l + 1. This dimension l determines the polynomial prefactor for exponentially small eigenvalue splitting.
