J. M. G. Gomez

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.

Misleading signatures of quantum chaos

The main signature of chaos in a quantum system is provided by spectral statistical analysis of the nearest-neighbor spacing distribution P(s) and the spectral rigidity given by the Delta(3)(L) statistic. It is shown that some standard unfolding procedures, such as local unfolding and Gaussian broadening, lead to a spurious saturation of Delta(3)(L) that spoils the relationship of this statistic with the regular or chaotic motion of the system. This effect can also be misinterpreted as Berrys saturation.

Stringent numerical test of the Poisson distribution for finite quantum integrable Hamiltonians

Using a class of exactly solvable models based on the pairing interaction, we show that it is possible to construct integrable Hamiltonians with a Wigner distribution of nearest-neighbor level spacings. However, these Hamiltonians involve many-body interactions and the addition of a small integrable perturbation very quickly leads the system to a Poisson distribution. Besides this exceptional case, we show that the accumulated distribution of an ensemble of random integrable two-body pairing Hamiltonians is in perfect agreement with the Poisson limit. These numerical results for quantum integrable Hamiltonians provide a further empirical confirmation of the work of Berry and Tabor in the semiclassical limit.

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.