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A Supersymmetry approach to billiards with randomly distributed scatterers

H. -J. Stoeckmann
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Abstract

The density of states for a chaotic billiard with randomly distributed point-like scatterers is calculated, doubly averaged over the positions of the impurities and the shape of the billiard. Truncating the billiard Hamiltonian to a N x N matrix, an explicit analytic expression is obtained for the case of broken time-reversal symmetry, depending on rank N of the matrix, number L of scatterers, and strength of the scattering potential. In the strong coupling limit a discontinuous change is observed in the density of states as soon as L exceeds N.

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H. -J. Stoeckmann. 2002-07-15. A Supersymmetry approach to billiards with randomly distributed scatterers. https://doi.org/10.1088/0305-4470%2F35%2F25%2F302

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