A Supersymmetry approach to billiards with randomly distributed scatterers

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.

References in corpus (2)

• Photon Localization in Resonant Media
• Singular statistics

Cited by in corpus (4)

• Derivation of determinantal structures for random matrix ensembles in a new way
• Distribution of Scattering Matrix Elements in Quantum Chaotic Scattering
• On the Efetov-Wegner terms by diagonalizing a Hermitian supermatrix
• A Supersymmetry Approach to Billiards with Randomly Distributed Scatterers II: Correlations