Semiclassical cross section correlations

Abstract

We calculate within a semiclassical approximation the autocorrelation function of cross sections. The starting point is the semiclassical expression for the diagonal matrix elements of an operator. For general operators with a smooth classical limit the autocorrelation function of such matrix elements has two contributions with relative weights determined by classical dynamics. We show how the random matrix result can be obtained if the operator approaches a projector onto a single initial state. The expressions are verified in calculations for the kicked rotor.

6 pages, 2 figures

References in corpus (5)

• Quantum Poincaré Recurrences
• The Spectral Autocorrelation Function in Weakly Open Chaotic Systems: Indirect Photodissociation of Molecules
• A diagrammatic approach for open chaotic systems
• Statistics of photodissociation spectra: nonuniversal properties
• Classical fluctuations and semiclassical matrix elements

Cited by in corpus (6)

• Semiclassical form factor for spectral and matrix element fluctuations of multi-dimensional chaotic systems
• Semiclassical Mechanism for the Quantum Decay in Open Chaotic Systems
• Semiclassical Theory for Decay and Fragmentation Processes in Chaotic Quantum Systems
• Open orbits and the semiclassical dwell time
• Fano interference and cross-section fluctuations in molecular photodissociation
• Correlations and fluctuations of matrix elements and cross sections