Accurate Semiclassical Spectral Asymptotics for a Two-Dimensional Magnetic Schrodinger Operator

作者：Helffer Bernard^*; Kordyukov Yuri A

来源：Annales Henri Poincare, 2015, 16(7): 1651-1688.

DOI：10.1007/s00023-014-0356-y

We revisit the problem of semiclassical spectral asymptotics for a pure magnetic Schrodinger 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 for some 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. V Nga >> ic have recently developed a different approach of the same problem.

• 出版日期2015-7