21811 articles – 15606 references  [version française]

hal-00462411, version 1

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

Abderemane Morame () 1, Francoise Truc () 2

(2010-03-09)

Abstract: 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. $

  • 1:  Laboratoire de Mathématiques Jean Leray (LMJL)
  • CNRS : UMR6629 – Université de Nantes – École Centrale de Nantes
  • 2:  Institut Fourier (IF)
  • CNRS : UMR5582 – Université Joseph Fourier - Grenoble I
  • Domain : Physics/Mathematical Physics
    Mathematics/Mathematical Physics
  • Keywords : Spectral asymptotics – magnetic field – Aharanov-Bohm – hyperbolic surface.
  • Internal note : IF_PREPUB
  • Available versions :  v1 (2010-04-29) v2 (2010-05-31)
 
  • hal-00462411, version 1
  • http://hal.archives-ouvertes.fr/hal-00462411
  • oai:hal.archives-ouvertes.fr:hal-00462411
  • From: Francoise Truc <>
  • Submitted on: Tuesday, 9 March 2010 15:43:07
  • Updated on: Thursday, 29 April 2010 15:58:26