Eigenvalues of Laplacian with constant magnetic field on non-compact hyperbolic surfaces with finite area

Details Eigenvalues of Laplacian with constant magnetic field on non-compact hyperbolic surfaces with finite area Eigenvalues of Laplacian with constant magnetic field on non-compact hyperbolic surfaces with finite area

2010-04-29

arxiv.org/abs/1004.5291v2

Physics

Mathematical Physics

Scientific paper

We consider a magnetic Laplacian $-\Delta_A=(id+A)^\star (id+A)$ on a noncompact hyperbolic surface $\mM $ with finite area. $A$ is a real one-form and the magnetic field $dA$ is constant in each cusp. When the harmonic component of $A$ satifies some quantified condition, the spectrum of $-\Delta_A$ is discrete. In this case we prove that the counting function of the eigenvalues of $-\Delta_{A}$ satisfies the classical Weyl formula, even when $dA=0. $

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