Abstract

Reflection of particles from a disordered or chaotic medium is characterized by a scattering matrix that can be represented as a superposition of resonances. Each resonance corresponds to an eigenstate in the medium and has a width related to the decay time of this eigenstate. We develop a general approach to study the distribution function of these decay times based on the nonlinear sigma model. We derive an integral representation of the distribution function that works equally well for systems of any symmetry and for any coupling to the measuring device. Our theory produces explicit analytic expressions for the distribution function in disordered metallic grains in the case of perfect coupling. These results are in perfect agreement with large-scale numerical simulations.