Analysis & PDE
- Anal. PDE
- Volume 3, Number 1 (2010), 49-80.
Poisson statistics for eigenvalues of continuum random Schrödinger operators
We show absence of energy levels repulsion for the eigenvalues of random Schrödinger operators in the continuum. We prove that, in the localization region at the bottom of the spectrum, the properly rescaled eigenvalues of a continuum Anderson Hamiltonian are distributed as a Poisson point process with intensity measure given by the density of states. In addition, we prove that in this localization region the eigenvalues are simple.
These results rely on a Minami estimate for continuum Anderson Hamiltonians. We also give a simple, transparent proof of Minami’s estimate for the (discrete) Anderson model.
Anal. PDE, Volume 3, Number 1 (2010), 49-80.
Received: 9 July 2009
Accepted: 6 August 2009
First available in Project Euclid: 20 December 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 82B44: Disordered systems (random Ising models, random Schrödinger operators, etc.)
Secondary: 47B80: Random operators [See also 47H40, 60H25] 60H25: Random operators and equations [See also 47B80]
Combes, Jean-Michel; Germinet, François; Klein, Abel. Poisson statistics for eigenvalues of continuum random Schrödinger operators. Anal. PDE 3 (2010), no. 1, 49--80. doi:10.2140/apde.2010.3.49. https://projecteuclid.org/euclid.apde/1513731040