1 research outputs found
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