Simplicity of Eigenvalues in the Anderson Model

@inproceedings{Klein2005SimplicityOE,
  title={Simplicity of Eigenvalues in the Anderson Model},
  author={Abel Klein and Stanislav Molchanov},
  year={2005}
}
We give a simple, transparent, and intuitive proof that all eigenvalues of the Anderson model in the region of localization are simple. The Anderson tight binding model is given by the random Hamiltonian Hω = −∆ + Vω on 2(Z), where ∆(x, y) = 1 if |x − y| = 1 and zero otherwise, and the random potential Vω = {Vω(x), x ∈ Zd} consists of independent identically distributed random variables whose common probability distribution μ has a bounded density ρ. It is known to exhibit exponential… CONTINUE READING
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