Weak-disorder expansion for the Anderson model on a tree

  title={Weak-disorder expansion for the Anderson model on a tree},
  author={Jeffrey D. Miller and Bernard Derridda},
  journal={Journal of Statistical Physics},
We show how certain properties of the Anderson model of a tree are related to the solutions of a nonlinear integral equation. Whether the wave function is extended or localized, for example, corresponds to whether or not the equation has a complex solution. We show how the equation can be solved in a weakdisorder expansion. We find that, for small disorder strength λ, there is an energyEc(λ) above which the density of states and the conducting properties vanish to all orders in perturbation… 

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