Tunneling, the Quillen metric and analytic torsion for high powers of a holomorphic line bundle

Robert J. Berman

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arXiv · 1106.2965

Tunneling, the Quillen metric and analytic torsion for high powers of a holomorphic line bundle

Robert J. Berman

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Abstract

Let L be a line bundle over a compact complex manifold X and endow L and TX with Hermitian metrics. Our main result provides a formula for the average distribution of the exponentially small eigenvalues of the corresponding Dolbeault Laplacians associated to high tensor powers of L; which in physics terminology is a measure of "tunneling" of the Dolbeault complex. Along the way a new proof of the asymptotics of the induced Quillen metric on the corresponding determinant line is obtained. A brief comparison with the tunneling effect for Witten Laplacians and large deviation principles for fermions is also made.

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BibTeX RIS

Robert J. Berman. 2011-06-15. Tunneling, the Quillen metric and analytic torsion for high powers of a holomorphic line bundle. https://arxiv.org/abs/1106.2965

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