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hal-00020307, version 1

Spectral analysis for adjacency operators on graphs

M. Mantoiu, S. Richard, R. Tiedra de Aldecoa 1

Annales Henri Poincaré (2007) ?

Abstract: We put into evidence graphs with adjacency operator whose singular subspace is prescribed by the kernel of an auxiliary operator. In particular, for a family of graphs called admissible, the singular continuous spectrum is absent and there is at most an eigenvalue located at the origin. Among other examples, the one-dimensional XY model of solid-state physics is covered. The proofs rely on commutators methods.

  • 1:  Laboratoire de Mathématiques d'Orsay (LM-Orsay)
  • CNRS : UMR8628 – Université Paris XI - Paris Sud
  • Domain : Mathematics/Mathematical Physics
    Physics/Mathematical Physics
  • Keywords : graph – adjacency operator – positive commutator – singular spectrum
  • Comment : 16 pages – 9 figures
 
  • hal-00020307, version 1
  • http://hal.archives-ouvertes.fr/hal-00020307
  • oai:hal.archives-ouvertes.fr:hal-00020307
  • From: Rafael Tiedra De Aldecoa <>
  • Submitted on: Wednesday, 8 March 2006 23:47:52
  • Updated on: Tuesday, 6 November 2007 09:44:18