On the spectrum of semi-classical Witten-Laplacians and Schrödinger operators in large dimension
On the spectrum of semi-classical Witten-Laplacians and Schrödinger operators in large dimension
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大维半经典维滕-拉普拉斯算子和薛定谔算子的谱
DOI：
10.1016/j.jfa.2004.11.010
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发表时间：
2005
影响因子：
1.7
通讯作者：
J. S. Møller
中科院分区：
文献类型：
--
作者：
O. Matte;J. S. Møller
研究了半经典极限下任意次形式下witten - laplacian的低洼谱，并在空间维度上一致。我们证明了在适当的假设下，暗示相函数有一个唯一的局部最小值，在谱的底部得到许多离散特征值簇。此外，我们能够计算每个簇中的特征值的数量。我们将结果应用于具有严格凸势的Schrödinger算子序列，并证明了半经典分析的一些著名结果在维数上也是一致成立的。
We investigate the low-lying spectrum of Witten–Laplacians on forms of arbitrary degree in the semi-classical limit and uniformly in the space dimension. We show that under suitable assumptions implying that the phase function has a unique local minimum one obtains a number of clusters of discrete eigenvalues at the bottom of the spectrum. Moreover, we are able to count the number of eigenvalues in each cluster. We apply our results to certain sequences of Schrödinger operators having strictly convex potentials and show that some well-known results of semi-classical analysis hold also uniformly in the dimension.