Semiclassical Asymptotics and Gaps in the Spectra of Periodic Schrödinger Operators with Magnetic Wells
نویسنده
چکیده
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 M such that H(M, R) = 0 equipped with a properly disconnected, cocompact action of a finitely generated, discrete group of isometries has an arbitrarily large number of spectral gaps in the semi-classical limit.
منابع مشابه
Spectral Gaps for Periodic Schrödinger Operators with Strong Magnetic Fields
We consider Schrödinger operators H = (ih d + A)∗(ih d + A) with the periodic magnetic field B = dA on covering spaces of compact manifolds. Under some assumptions on B, we prove that there are arbitrarily large number of gaps in the spectrum of these operators in the semiclassical limit of strong magnetic field h → 0.
متن کاملSpectral Gaps for Periodic Schrödinger Operators with Hypersurface Magnetic Wells
We consider a periodic magnetic Schrödinger operator on a noncompact Riemannian manifold M such that H(M, R) = 0 endowed with a properly discontinuous cocompact isometric action of a discrete group. We assume that there is no electric field and that the magnetic field has a periodic set of compact magnetic wells. We review a general scheme of a proof of existence of an arbitrary large number of...
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In this paper, we study an L version of the semiclassical approximation of magnetic Schrödinger operators with invariant Morse type potentials on covering spaces of compact manifolds. In particular, we are able to establish the existence of an arbitrary large number of gaps in the spectrum of these operators, in the semiclassical limit as the coupling constant μ goes to zero.
متن کاملm at h . SP ] 1 8 M ar 2 00 1 SEMICLASSICAL ASYMPTOTICS AND GAPS IN THE SPECTRA OF MAGNETIC SCHRÖDINGER OPERATORS
In this paper, we study an L version of the semiclassical approximation of magnetic Schrödinger operators with invariant Morse type potentials on covering spaces of compact manifolds. In particular, we are able to establish the existence of an arbitrary large number of gaps in the spectrum of these operators, in the semiclassical limit as the coupling constant μ goes to zero.
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In this paper, we study an L version of the semiclassical approximation of magnetic Schrödinger operators with invariant Morse type potentials on covering spaces of compact manifolds. In particular, we are able to establish the existence of an arbitrary large number of gaps in the spectrum of these operators, in the semiclassical limit as the coupling constant μ goes to zero.
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