Accurate semiclassical spectral asymptotics for a two-dimensional magnetic Schrödinger operator

Abstract

We revisit the problem of semiclassical spectral asymptotics for a pure magnetic Schrödinger operator on a two-dimensional Riemannian manifold. We suppose that the minimal value $b_0$ of the intensity of the magnetic field is strictly positive, and the corresponding minimum is unique and non-degenerate. The purpose is to get the control on the spectrum in an interval $(h{b}_0,h(b_0+{\gamma }_0)]$ for some ${\gamma }_0>0$ independent of the semiclassical parameter $h$. The previous papers by Helffer-Mohamed and by Helffer-Kordyukov were only treating the ground-state energy or a finite (independent of $h$) number of eigenvalues. Note also that N. Raymond and S. Vu Ngoc have recently developed a different approach of the same problem.

37 pages

Cited by in corpus (2)

• Little Magnetic Book
• Semiclassical eigenvalue asymptotics for the Bochner Laplacian of a positive line bundle on a symplectic manifold