E. Faleiro

Theoretical derivation of 1/f noise in quantum chaos

It was recently conjectured that 1/f noise is a fundamental characteristic of spectral fluctuations in chaotic quantum systems. This conjecture is based on the power spectrum behavior of the excitation energy fluctuations, which is different for chaotic and integrable systems. Using random matrix theory, we derive theoretical expressions that explain without free parameters the universal behavior of the excitation energy fluctuations power spectrum. The theory gives excellent agreement with numerical calculations and reproduces to a good approximation the 1/f (1/f(2)) power law characteristic of chaotic (integrable) systems. Moreover, the theoretical results are valid for semiclassical systems as well.

1/f^a^l^p^h^a Noise in Spectral Fluctuations of Quantum Systems

The power law 1/f(alpha) in the power spectrum characterizes the fluctuating observables of many complex natural systems. Considering the energy levels of a quantum system as a discrete time series where the energy plays the role of time, the level fluctuations can be characterized by the power spectrum. Using a family of quantum billiards, we analyze the order-to-chaos transition in terms of this power spectrum. A power law 1/f(alpha) is found at all the transition stages, and it is shown that the exponent alpha is related to the chaotic component of the classical phase space of the quantum system.

Shell-Model studies of chaos and statistical properties in nuclei

Shell-model calculations with realistic empirical interactions constitute an excellent tool to study statistical properties of nuclei. Using large-scale shell-model calculations in pf- shell nuclei, we study how the onset of chaos depends on different properties of the nuclear interaction and on excitation energy. We make use of classical random matrix theory and other theoretical developments based on information theory and time series analysis. We show that besides energy-level statistics, other statistical properties like the complexity of wave functions are fundamental for a proper determination of the dynamical regime of nuclei. Important deviations from GOE are observed in level fluctuations and in the complexity of wave functions.

Recent results in quantum chaos and its applications to atomic nuclei

A survey of chaotic dynamics in atomic nuclei is presented, using on the one hand standard statistics of quantum chaos studies, and on the other a new approach based on time series analysis methods. The study of shell-model spectra in the pf shell shows that nuclear chaos is strongly isopin dependent and increases with excitation energy. On the other hand, it is found that chaotic quantum systems exhibit 1/f noise and regular systems exhibit 1/f2 behaviour. It is shown that the time series approach can be used to calculate quite accurately the fraction of missing levels and the existence of mixed symmetries in experimental level spectra.

Gamma-hadron discrimination by the multifractal spectrum of 1/f density fluctuations in extensive air showers

Abstract High-energy interactions of cosmic γ rays and protons and also helium, oxygen and iron nuclei with the Earth atmosphere have been simulated by means of the CORSIKA Monte Carlo code, and the secondary-particle density distributions at ground level in the resulting extensive air showers (EAS) have been studied. It is shown that the fluctuations of the particle density distributions have features typical of a 1/f noise. The multifractal spectrum of the samples is obtained and is found to have different features for different primary cosmic rays. This property is applied to the separation of electromagnetic from hadronic simulated EAS and it is proposed as a discrimination method when real data are available. A cutting parameter related to the multifractal spectrum is calculated and the efficiency of the cutting procedure for γ-hadron separation is evaluated.

Principal Components Analysis of Extensive Air Showers Applied to the Identification of Cosmic TeV Gamma-Rays

We apply a principal components analysis (PCA) to the secondary particle density distributions at ground level produced by cosmic γ-rays and protons. For this purpose, high-energy interactions of cosmic rays with Earths atmosphere and the resulting extensive air showers have been simulated by means of the CORSIKA Monte Carlo code. We show that a PCA of the two-dimensional particle density fluctuations provides a decreasing sequence of covariance matrix eigenvalues that have typical features of a polynomial law, which are different for different primary cosmic rays. This property is applied to the separation of electromagnetic showers from proton simulated extensive air showers, and it is proposed as a new discrimination method that can be used experimentally for γ-proton separation. A cutting parameter related to the polynomial behavior of the decreasing sequence of covariance matrix eigenvalues is calculated, and the efficiency of the cutting procedure for γ-proton separation is evaluated.

Perspectives on 1/f noise in quantum chaos

The power spectrum of the ?n statistic of quantum spectra presents 1/f? noise. For chaotic systems ? = 1 while for regular systems ? = 2. Although the transition from regularity to chaos is non universal, for a wide variety of systems with a mixed phase space the value of ? is intermediate between 1 and 2 and can be related to the fraction of regular or chaotic orbits in the total phase space. This statistic can be a very useful tool for the analysis of experimental spectra, specially in the case of missing levels or spectral sequences with mixed symmetries.