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

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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 b₀ 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 (hb₀, h(b₀ +γ₀)] for some γ₀>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.