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Anderson Model


The Anderson model is a random linear operator obtained by adding a random diagonal potential to a graph adjacency or lattice hopping linear operator. In the adjacency convention,

 H=A+wdiag(omega_v),

where A is the adjacency matrix, w is the disorder strength, and the potentials omega_v are independent random variables with a specified law. The graph and potential distributions must both be specified.


See also

Operator Spectrum, Random Matrix, Schrödinger Operator

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References

Kirsch, W. "An Invitation to Random Schrödinger Operators." With an appendix by F. Klopp. In Opérateurs de Schrödinger aléatoires. Paris, France: Société Mathématique de France, pp. 1-119, 2008. https://arxiv.org/abs/0709.3707.

Cite this as:

Weisstein, Eric W. "Anderson Model." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/AndersonModel.html

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