Statistics of resonance poles, phase shifts and time delays in quantum chaotic scattering: Random matrix approach for systems with broken time-reversal invariance
- Fachbereich Physik, Universitaet-GH Essen, D-45117 Essen (Germany)
Assuming the validity of random matrices for describing the statistics of a {ital closed} chaotic quantum system, we study analytically some statistical properties of the S-matrix characterizing scattering in its {ital 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 Mopen channels; a=1,2,{hor_ellipsis},M. A physical realization of this case corresponds to the chaotic scattering in ballistic microstructures pierced by a strong enough magnetic flux. By using the supersymmetry method we derive an explicit expression for the density of S-matrix poles (resonances) in the complex energy plane. When all scattering channels are considered to be equivalent our expression describes a crossover from the {chi}{sup 2} distribution of resonance widths (regime of isolated resonances) to a broad power-like distribution typical for the regime of overlapping resonances. The first moment is found to reproduce exactly the Moldauer{endash}Simonius relation between the mean resonance width and the transmission coefficient. Under the same assumptions we derive an explicit expression for the parametric correlation function of densities of eigenphases {theta}{sub a} of the S-matrix (taken modulo 2{pi}). We use it to find the distribution of derivatives {tau}{sub a}={partial_derivative}{theta}{sub a}/{partial_derivative}E of these eigenphases with respect to the energy (``partial delay times``) as well as with respect to an arbitrary external parameter. We also find the parametric correlations of the Wigner{endash}Smith time delay {tau}{sub w}(E)=(1/M){summation}{sub a}{partial_derivative}{theta}{sub a}/{partial_derivative}E at two different energies E{minus}{Omega}/2 and E+{Omega}/2 as well as at two different values of the external parameter. (Abstract Truncated)
- OSTI ID:
- 538905
- Journal Information:
- Journal of Mathematical Physics, Vol. 38, Issue 4; Other Information: PBD: Apr 1997
- Country of Publication:
- United States
- Language:
- English
Similar Records
Impact of alternative transmission coeffcient parameterizations on Hauser-Feshbach theory
Projection-operator calculations for shape resonances: A new method based on the many-body optical-potential approach