Random matrix description of decaying quantum systems
arXiv:nlin/0510005 · doi:10.1088/0305-4470/38/49/020
Abstract
This contribution describes a statistical model for decaying quantum systems (e.g. photo-dissociation or -ionization). It takes the interference between direct and indirect decay processes explicitely into account. The resulting expressions for the partial decay amplitudes and the corresponding cross sections may be considered a many-channel many-resonance generalization of Fano's original work on resonance lineshapes [Phys. Rev 124, 1866 (1961)]. A statistical (random matrix) model is then introduced. It allows to describe chaotic scattering systems with tunable couplings to the decay channels. We focus on the autocorrelation function of the total (photo) cross section, and we find that it depends on the same combination of parameters, as the Fano-parameter distribution. These combinations are statistical variants of the one-channel Fano parameter. It is thus possible to study Fano interference (i.e. the interference between direct and indirect decay paths) on the basis of the autocorrelation function, and thereby in the regime of overlapping resonances. It allows us, to study the Fano interference in the limit of strongly overlapping resonances, where we find a persisting effect on the level of the weak localization correction.
arXiv comment16 pages, 2 figures
References in corpus (19)
- Random Matrix Theories in Quantum Physics: Common Concepts
- Statistics of resonance poles, phase shifts and time delays in quantum chaotic scattering for systems with broken time reversal invariance
- Fano Resonance in a Quantum Wire with a Side-coupled Quantum Dot
- Coulomb-Modified Fano Resonance in a One-Lead Quantum Dot
- Fano resonances as a probe of phase coherence in quantum dots
- Interference Phenomena in Electronic Transport Through Chaotic Cavities: An Information-Theoretic Approach
- Spectra of Random Contractions and Scattering Theory for Discrete-Time Systems
- Dynamical model for the quantum-to-classical crossover of shot noise
- Fingerprints of classical diffusion in open 2D mesoscopic systems in the metallic regime
- Photo-ionization of the helium atom close to the double ionization threshold: towards the Ericson regime
- Recovery of the fidelity amplitude for the Gaussian ensembles
- Signatures of the correlation hole in total and partial cross sections
- Photodissociation in Quantum Chaotic Systems: Random Matrix Theory of Cross-Section Fluctuations
- Interfering Doorway States and Giant Resonances. II: Transition Strengths
- The Spectral Autocorrelation Function in Weakly Open Chaotic Systems: Indirect Photodissociation of Molecules
- A diagrammatic approach for open chaotic systems
- Statistical Properties of Fano Resonances in Atomic and Molecular Photoabsorption
- Statistics of photodissociation spectra: nonuniversal properties
- The decay of photoexcited quantum systems: a description within the statistical scattering model