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math.SP2009★ 11 cited
Probabilistic Weyl laws for quantized tori
T. J. Christiansen, M. Zworski
For the Toeplitz quantization of complex-valued functions on a -dimensional torus we prove that the expected number of eigenvalues of small random perturbations of a quantized…
math-ph2009
A mathematical formulation of the Mahaux-Weidenmüller formula for the scattering matrix
T. J. Christiansen, M. Zworski
The purpose of this note is to give a mathematical explanation of a formula for the scattering matrix for a manifold with infinite cylindrical ends or a waveguide. This formula, wh…