Abstract
Exact analytical expressions for the cross-section correlation functions of chaotic scattering systems have hitherto been derived only under special conditions. The objective of the present article is to provide expressions that are applicable beyond these restrictions. The derivation is based on a statistical model of Breit-Wigner type for chaotic scattering amplitudes which has been shown to describe the exact analytical results for the scattering (S)-matrix correlation functions accurately. Our results are given in the energy and in the time representations and apply in the whole range from isolated to overlapping resonances. The S-matrix contributions to the cross-section correlations are obtained in terms of explicit irreducible and reducible correlation functions. Consequently, the model can be used for a detailed exploration of the key features of the cross-section correlations and the underlying physical mechanisms. In the region of isolated resonances, the cross-section correlations contain a dominant contribution from the self-correlation term. For narrow states the self-correlations originate predominantly from widely spaced states with exceptionally large partial width. In the asymptotic region of well-overlapping resonances, the cross-section autocorrelation functions are given in terms of the S-matrix autocorrelation functions. For inelastic correlations, in particular, the Ericson fluctuations rapidly dominate in that region. Agreement with known analytical and experimental results is excellent.
Highlights
Scattering processes from highly complex systems show characteristic fluctuation phenomena [1,2,3]
The aim of the present article has been to obtain an analytical approximation to the cross-section correlations and related functions for a chaotic scattering system
The analysis was based on the statistical Breit-Wigner (SBW) model, extensively used previously in the asymptotic limits of narrow and strongly overlapping resonances
Summary
Scattering processes from highly complex systems show characteristic fluctuation phenomena [1,2,3]. The SBW model approximates the S matrix by a coherent sum of resonances with random partial width amplitudes of appropriate average strength and a total width given by the sum of the partial widths associated with the open channels It yields a remarkably good description for the S-matrix autocorrelations [31]. We first extend them by deriving the SBW expressions for the S-matrix and cross-section autocorrelation functions both in the energy and in the time representation Their usefulness and accuracy is established numerically by comparison with known exact results derived within RMT on the basis of the supersymmetry method [24,25,27]. We demonstrate explicitly the central role played by the channels for which the scattering signal is recorded
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