Distribution of Off-Diagonal Cross Sections in Quantum Chaotic Scattering: Exact Results and Data Comparison

Abstract

The recently derived distributions for the scattering-matrix elements in quantum chaotic systems are not accessible in the majority of experiments, whereas the cross sections are. We analytically compute distributions for the off-diagonal cross sections in the Heidelberg approach, which is ap- plicable to a wide range of quantum chaotic systems. We thus eventually fully solve a problem which already arose more than half a century ago in compound-nucleus scattering. We compare our results with data from microwave and compound-nucleus experiments, particularly addressing the transition from isolated resonances towards the Ericson regime of strongly overlapping ones.

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• Missing-level statistics in classically chaotic quantum systems with symplectic symmetry
• Resonance eigenfunction hypothesis for chaotic systems
• Distributions of the Wigner reaction matrix for microwave networks with symplectic symmetry in the presence of absorption
• Experimental investigation of distributions of the off-diagonal elements of the scattering and the Wigner's $\hat{K}$ matrices for networks with broken time reversal invariance
• Reflection Time Difference as a probe of S-matrix Zeroes in Chaotic Resonance Scattering
• Wave scattering properties of multiple weakly-coupled complex systems
• Implementing Non-Universal Features with a Random Matrix Theory Approach: Application to Space-to-Configuration Multiplexing
• Experimental study of closed and open microwave waveguide graphs with preserved and partially violated time-reversal invariance
• Experimental investigation of the fluctuations in nonchaotic scattering in microwave billiards
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• Semiclassical approach to $S$ matrix energy correlations and time delay in chaotic systems
• Closed and open superconducting microwave waveguide networks as a model for quantum graphs
• Experimental study of the distributions of off-diagonal scattering-matrix elements of quantum graphs with symplectic symmetry
• Universality Emerging in a Universality: Derivation of the Ericson Transition in Stochastic Quantum Scattering and Experimental Validation
• Diffuse field cross-correlations: scattering theory and electromagnetic experiments