- 03-448 Oliver Matte and Jacob Schach Moeller
- On the spectrum of semi-classical Witten-Laplacians and Schroedinger
operators in large dimension
(121K, latex)
Oct 1, 03
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Abstract. 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 minimum one obtains a number of bands of
discrete eigenvalues at the bottom of the spectrum. Moreover we are able
to count the number of eigenvalues in each band. We apply our results to
certain sequences of Schroedinger operators having strictly convex
potentials and show that some well-known results of semi-classical
analysis hold also uniformly in the dimension.
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