Communications in Mathematical Physics

, Volume 164, Issue 3, pp 489–505 | Cite as

Pure point spectrum under 1-parameter perturbations and instability of Anderson localization

  • A. Ya. Gordon


We consider a selfadjoint operator,A, and a selfadjoint rank-one projection,P, onto a vector, φ, which is cyclic forA. We study the set of all eigenvalues of the operatorA t =A+tP (t∈∝) that belong to its essential spectrum (which does not depend on the parametert). We prove that this set is empty for a dense set of values oft. Then we apply this result or its idea to questions of Anderson localization for 1-dimensional Schrödinger operators (discrete and continuous).


Neural Network Statistical Physic Complex System Nonlinear Dynamics Quantum Computing 
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Copyright information

© Springer-Verlag 1994

Authors and Affiliations

  • A. Ya. Gordon
    • 1
  1. 1.Warshavskoye shosseMITPANMoscowRussia

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