Semiclassical Spectral Asymptotics and Geometry of Magnetic Fields

Yuri A. Kordyukov - Ufa, Rusia

Resumo:

In this talk, we describe our recent results obtained in joint work with B. Helffer on semiclassical asymptotics of the low-lying eigenvalues of a magnetic Schroedinger operator on a compact Riemannian manifold in the case when the magnetic field does not vanish at each point. We give geometric interpretations of our results and discuss some related problems in differential geometry. Finally, we describe applications to the problem of the existence of spectral gaps in the corresponding periodic setting.

© Yuri A. Kordyukov.