Abstract
We investigate simple open few-body systems, the spectra of which exhibit fluctuating patterns, and review the conditions for the existence of an Ericson regime in deterministic, open quantum systems. A widely used criterion, the Lorentzian shape of the autocorrelation function of the spectrum, is shown to be insufficient for the occurrence of Ericson fluctuations: integrable systems or open systems that are not in the Ericson regime might display such an autocorrelation function. We also investigate the sensitivity of Ericson fluctuations on simplified models of realistic systems. In particular, we show that a simplified hydrogenic model for alkali atoms in crossed magnetic and electric fields does not yield Ericson fluctuations for a choice of the energy and field parameters where the realistic system is in the Ericson regime.
Highlights
We investigate simple open few-body systems, the spectra of which exhibit fluctuating patterns, and review the conditions for the existence of an Ericson regime in deterministic, open quantum systems
Ericson [14] showed that a spectrum of overlapping resonances with Lorentzian or Fano profiles leads to a Lorentzian shape of the autocorrelation function, where the width of this function is the mean width of the resonances
We show that the autocorrelation function of the photoionization cross-section again has a Lorentzian shape, despite the fact that the Ericson regime is not reached
Summary
The Ericson regime in chaotic scattering is completely characterized by strong overlapping of the resonances; that is, the mean width ̄ of the resonances must be much larger than the mean level spacing s, ̄/s 1. This observation is important for answering the question of whether a Lorentzian autocorrelation function is caused by irregular scattering, or rather indicates a universal behavior in the presence of external fields (as proposed in [44]) Distinguishing between these two scenarios is a serious experimental problem, since the strict validation of the Ericson condition in terms of complex poles requires us to determine these poles, which cannot be achieved experimentally for overlapping resonances. At a given energy, structures in the LDOS arise from a superposition of modulations from several Landau levels En,k This situation can be thought of as an overlap of the sidebands (n, k) from different major quantum numbers n. We conclude that a Lorentzian autocorrelation function seems to be a generic feature of equation (4) and is not necessarily related to chaotic scattering
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