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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