A supersymmetry approach to billiards with randomly distributed scatterers
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Publication:4465870
DOI10.1088/0305-4470/35/25/302zbMATH Open1049.81031arXivcond-mat/0207351OpenAlexW3125526591MaRDI QIDQ4465870
Publication date: 9 June 2004
Published in: Journal of Physics A: Mathematical and General (Search for Journal in Brave)
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.
Full work available at URL: https://arxiv.org/abs/cond-mat/0207351
Quantum chaos (81Q50) Disordered systems (random Ising models, random Schrödinger operators, etc.) in equilibrium statistical mechanics (82B44) Quantum equilibrium statistical mechanics (general) (82B10)
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