CORRELATIONS BETWEEN RESONANCES IN A STATISTICAL SCATTERING MODEL

The distortion of the regular motion in a quantum system by its coupli ng to the continuum of decay channels is investigated. The regular mot ion is described by means of a Poissonian ensemble. We focus on the ca se of only a few channels K<10. The coupling to the continuum induces two main effects, due to which the distorted system differs from a cha otic system (described by a Gaussian ensemble): (i) The width distribu tion for large coupling becomes broader than the corresponding chi(K)( 2) distribution in the Gaussian orthogonal ensemble case. (ii) Due to the coupling to the continuum, correlations are induced not only betwe en the positions of the resonances but also between positions and widt hs. These correlations remain even in the strong coupling limit. In or der to explain these results, we relate the width of a trapped resonan ce state to the distance between its neighboring levels and derive an asymptotic expression for the width distribution for the one channel c ase.