1997/01/07 by Yan. V. Fyodorov, H. -J. Sommers · 1 citation
Physics and Astronomy · #cond-mat.mes-hall #chao-dyn #nlin.CD
paper · pdf · doi:10.1063/1.531919
published as J.Math.Phys. v.38 ,1918 (1997) · 51 pages, RevTEX , three figures are available on request. To be published in the special issue of the Journal of Mathematical Physics
arxiv created 1997/01/07 · arxiv updated 2016/08/31
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.