Mikhail Kurilov: Density of scattering resonances in a disordered system

The system under study consists of a disordered system and an M-channel ballistic lead connected to it. The reflection of waves incident on the disordered part is described by the S matrix. We are interested in the statistics of resonance widths (i.e., imaginary parts of the poles of the S matrix). Using the framework of a supersymmetric nonlinear sigma model we derive general formulas of the resonance widths distribution for all three Wigner-Dyson classes and calculate it in the zero-dimensional limit for the case of identical transmission coefficients. Obtained formulas are in a good agreement with numerical RMT simulations.