Localization for Schrödinger operators with Poisson random potential | Zendy

François Germinet | Zendy; Peter D. Hislop | Zendy; Abel Klein | Zendy

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Localization for Schrödinger operators with Poisson random potential

Author(s) -

François Germinet,

Peter D. Hislop,

Abel Klein

Publication year - 2007

Publication title -

journal of the european mathematical society

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 3.549

H-Index - 64

eISSN - 1435-9863

pISSN - 1435-9855

DOI - 10.4171/jems/89

Subject(s) - mathematics , schrödinger's cat , poisson distribution , pseudodifferential operators , pure mathematics , mathematical physics , statistics

We prove exponential and dynamical localization for the Schrodinger operator with a nonnegative Poisson random potential at the bottom of the spectrum in any dimension. We also conclude that the eigenvalues in that spectral region of localization have finite multiplicity. We prove similar localization results in a prescribed energy interval at the bottom of the spectrum provided the density of the Poisson process is large enough.

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