Physics – Condensed Matter – Disordered Systems and Neural Networks
Scientific paper
1997-02-12
Physics
Condensed Matter
Disordered Systems and Neural Networks
31 pages, 7 eps figures, LaTeX document using AMS symbols (amssym.def, amssym.tex)
Scientific paper
We develop a polymer expansion with large/small field conditions for the mean resolvent of a weakly disordered system. Then we show that we can apply our result to a two-dimensional model, for energies outside the unperturbed spectrum or in the free spectrum provided the potential has an infra-red cut-off. This leads to an asymptotic expansion for the density of states. We believe this is an important first step towards a rigourous analysis of the density of states in the free spectrum of a random Schr\"odinger operator at weak disorder.
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