15 citations · 37 across the 11 of their papers we have counts for
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Semiclassical analysis of Schrödinger operators with magnetic wells
Bernard Helffer, Yuri A. Kordyukov
We give a survey of some results, mainly obtained by the authors and their collaborators, on spectral properties of the magnetic Schrödinger operators in the semiclassical limit. W…
Spectral gaps for periodic Schrödinger operators with hypersurface magnetic wells: Analysis near the bottom
B. Helffer, Y. A. Kordyukov
We consider a periodic magnetic Schrödinger operator , depending on the semiclassical parameter , on a noncompact Riemannian manifold such that $H^1(M, {\mathbb R})=0…
Spectral gaps for periodic Schrödinger operators with hypersurface magnetic wells
Bernard Helffer, Yuri A. Kordyukov
We consider a periodic magnetic Schrödinger operator on a noncompact Riemannian manifold such that $H^1(M, \RR)=0$ endowed with a properly discontinuous cocompact isometric act…
The periodic magnetic Schrödinger operators: spectral gaps and tunneling effect
Bernard Helffer, Yuri A. Kordyukov
A periodic Schrödinger operator on a noncompact Riemannian manifold such that endowed with a properly discontinuous cocompact isometric action of a discre…
Semiclassical asymptotics and gaps in the spectra of periodic Schrödinger operators with magnetic wells
Bernard Helffer, Yuri A. Kordyukov
We show that, under some very weak assumption of effective variation for the magnetic field, a periodic Schrödinger operator with magnetic wells on a noncompact Riemannian manifold…