Semiclassical eigenvalue asymptotics for the Bochner Laplacian of a positive line bundle on a symplectic manifold

Abstract

We consider the Bochner Laplacian on high tensor powers of a positive line bundle on a closed symplectic manifold (or, equivalently, the semiclassical magnetic Schrödinger operator with the non-degenerate magnetic field). We assume that the operator has discrete wells. The main result of the paper states asymptotic expansions for its low-lying eigenvalues.

24 pages. arXiv admin note: text overlap with arXiv:1809.06799

References in corpus (2)

• Semiclassical spectral analysis of Toeplitz operators on symplectic manifolds: the case of discrete wells
• A semiclassical Birkhoff normal form for symplectic magnetic wells

Cited by in corpus (1)

• The spectral density function of the renormalized Bochner Laplacian on a symplectic manifold