Statistics of resonance poles, phase shifts and time delays in quantum chaotic scattering for systems with broken time reversal invariance

Assuming the validity of random matrices for describing the statistics of a closed chaotic quantum system, we study analytically some statistical properties of the S-matrix characterizing scattering in its open counterpart. In the first part of the paper we attempt to expose systematically ideas underlying the so-called stochastic (Heidelberg) approach to chaotic quantum scattering. Then we concentrate on systems with broken time-reversal invariance coupled to continua via M open channels. By using the supersymmetry method we derive: (i) an explicit expression for the density of S-matrix poles (resonances) in the complex energy plane (ii) an explicit expression for the parametric correlation function of densities of eigenphases of the S-matrix. We use it to find the distribution of derivatives of these eigenphases with respect to the energy ("partial delay times" ) as well as with respect to an arbitrary external parameter.Comment: 51 pages, RevTEX , three figures are available on request. To be published in the special issue of the Journal of Mathematical Physic

Random Matrices close to Hermitian or unitary: overview of methods and results

The paper discusses progress in understanding statistical properties of complex eigenvalues (and corresponding eigenvectors) of weakly non-unitary and non-Hermitian random matrices. Ensembles of this type emerge in various physical contexts, most importantly in random matrix description of quantum chaotic scattering as well as in the context of QCD-inspired random matrix models.Comment: Published version, with a few more misprints correcte