Person:
Relaño Pérez, Armando

First Name

Armando

Last Name

Relaño Pérez

URI

https://hdl.handle.net/20.500.14352/75045

Affiliation

Universidad Complutense de Madrid

Faculty / Institute

Ciencias Físicas

Department

Estructura de la Materia, Física Térmica y Electrónica

Area

Física Aplicada

Identifiers

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Now showing 1 - 9 of 9

Chaos and 1/f noise in nuclear spectra
(Key Topics in Nuclear Structure: Proceedings of the 8th International Spring Seminar on Nuclear Physics Paestum, Italy, 23 – 27 May 2004, 2005) Gómez, J. M. G.; Faleiro, E.; Molina, R. A.; Muñoz, L.; Relaño Pérez, Armando; Covello, Aldo
Many complex systems in nature and in human society exhibit time fluctuations characterized by a power spectrum S(f) which is a power function of the frequency f . Examples with this behavior are the Sun spot activity, the human heartbeat, the DNA sequence, or Bach’s First Brandenburg Concert. In this work, we show that the energy spectrum fluctuations of quantum systems can be formally considered as a discrete time series, with energy playing the role of time. Because of this analogy, the fluctuations of quantum energy spectra can be studied using traditional methods of time series, like calculating the Fourier transform and studying the power spectrum. We present the results for paradigmatic quantum chaotic systems like atomic nuclei (by means of large scale shell-model calculations) and the predictions of random matrix theory. We have found a surprising general property of quantum systems: The energy spectra of chaotic quantum systems are characterized by 1= f noise, while regular quantum systems exhibit 1= f^2 noise. Some other interesting applications of this time series analogy are a test of the existence of quantum chaos remnants in the nuclear masses, and the study of the order to chaos transition in semiclassical systems. In this case, it is found that the energy level spectrum exhibits 1= f^α noise with the exponent changing smoothly from α = 2 in regular systems to α= 1 in chaotic systems.
Spectral statistics in noninteracting many-particle systems
(Physical Review E, 2006) Relaño Pérez, Armando; Muñoz, L.; Faleiro, E.; Molina, R. A.; Retamosa Granado, Joaquín
It is widely accepted that the statistical properties of energy level spectra provide an essential characterization of quantum chaos. Indeed, the spectral fluctuations of many different systems like quantum billiards, atoms, or atomic nuclei have been studied. However, noninteracting many-body systems have received little attention, since it is assumed that they must exhibit Poisson-like fluctuations. Apart from a heuristic argument of Bloch, there are neither systematic numerical calculations nor a rigorous derivation of this fact. Here we present a rigorous study of the spectral fluctuations of noninteracting identical particles moving freely in a mean field emphasizing the evolution with the number of particles N as well as with the energy. Our results are conclusive. For N >= 2 the spectra of these systems exhibit Poisson fluctuations provided that we consider sufficiently high excitation energies. Nevertheless, when the mean field is chaotic there exists a critical energy scale L-c; beyond this scale, the fluctuations deviate from the Poisson statistics as a reminiscence of the statistical properties of the mean field.
Power-spectrum characterization of the continuous Gaussian ensemble
(Physical Review E, 2008) Relaño Pérez, Armando; Muñoz, L.; Retamosa Granado, Joaquín; Faleiro, E.; Molina, R. A.
The continuous Gaussian ensemble, also known as the nu-Gaussian or nu-Hermite ensemble, is a natural extension of the classical Gaussian ensembles of real (nu= 1), complex (nu= 2), or quaternion (nu=4) matrices, where nu is allowed to take any positive value. From a physical point of view, this ensemble may be useful to describe transitions between different symmetries or to describe the terrace-width distributions of vicinal surfaces. Moreover, its simple form allows one to speed up and increase the efficiency of numerical simulations dealing with large matrix dimensions. We analyze the long-range spectral correlations of this ensemble by means of the delta(n) statistic. We derive an analytical expression for the average power spectrum of this statistic, <(P(k)(delta))over bar>, based on approximated forms for the two-point cluster function and the spectral form factor. We find that the power spectrum of delta(n) evolves from <(P(k)(delta))over bar> proportional to 1/ k at nu= 1 to <(P(k)(delta))over bar> proportional to 1/ k(2) at nu= 0. Relevantly, the transition is not homogeneous with a 1/ f alpha noise at all scales, but heterogeneous with coexisting 1/ f and 1/ f(2) noises. There exists a critical frequency k(c)proportional to nu that separates both behaviors: below k(c), <(P(k)(delta))over bar> follows a 1/f power law, while beyond kc, it transits abruptly to a 1/ f(2) power law. For nu>1 the 1/ f noise dominates through the whole frequency range, unveiling that the 1/ f correlation structure remains constant as we increase the level repulsion and reduce to zero the amplitude of the spectral fluctuations. All these results are confirmed by stringent numerical calculations involving matrices with dimensions up to 10(5).
Theoretical derivation of 1/ƒ noise in quantum chaos
(Physical review letters, 2004) Relaño Pérez, Armando; Faleiro, E.; Gómez Gómez, José María; Molina, R. A.; Muñoz, L.; Retamosa Granado, Joaquín
It was recently conjectured that 1/ƒ 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/ƒ (1/ƒ^(2)) power law characteristic of chaotic (integrable) systems. Moreover, the theoretical results are valid for semiclassical systems as well.
Shell-Model studies of chaos and statistical properties in nuclei
(Journal of Physics: Conference Series, 11TH International spring seminar on nuclear physics: shell model and nuclear structure, 2015) Gómez Gómez, José María; Faleiro, E.; Muñoz, L.; Molina, R. A.; Relaño Pérez, Armando
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.
Power spectrum of nuclear spectra with missing levels and mixed symmetries
(Physics Letters B, 2007) Relaño Pérez, Armando; Molina, R. A.; Retamosa Granado, Joaquín; Muñoz, L.; Faleiro, E.
Sequences of energy levels in nuclei are often plagued with missing levels whose number and position are unknown. It is also quite usual that all the quantum numbers of certain levels cannot be experimentally determined, and thus levels of different symmetries are mixed in the same sequence. The analysis of these imperfect spectra (from the point of view of spectral statistics) is unavoidable if one wants to extract some statistical information. The power spectrum of the delta(q) statistic has emerged in recent years as an important tool for the study of quantum chaos and spectral statistics. We derive analytical expressions for the observed power spectrum in terms of the fraction of observed levels and the number of mixed sequences. These expressions are tested with large shell model spectra simulating realistic experimental situations. A good estimation of the number of mixed symmetries and the fraction of missing levels is obtained by means of a least-squares fit in a wide set of different situations.
Recent results in quantum chaos and its applications to atomic nuclei
(Journal of Physics: Conference Series, 2011) Relaño Pérez, Armando; Gömez Gómez, José María; Faleiro, E.; Muñoz, L.; Molina, R. A.; Retamosa Granado, J.
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/f(2) 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.
Principal components analysis of extensive air showers applied to the identification of cosmic TeV gamma-rays
(Astrophysical journal supplement series, 2004) Faleiro, E.; Gómez Gómez, José María; Muñoz, L.; Relaño Pérez, Armando; Retamosa Granado, Joaquín
We apply a principal components analysis (PCA) to the secondary particle density distributions at ground level produced by cosmic gamma-rays and protons. For this purpose, high-energy interactions of cosmic rays with Earth's 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 gamma-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 gamma-proton separation is evaluated.
Perspectives on 1/ƒ noise in quantum chaos
(Journal of physics: Conference series, 2010) Relaño Pérez, Armando; Molina, R. A.; Retamosa Granado, Joaquín; Muñoz, L.; Faleiro, E.; Gómez Gómez, José María
The power spectrum of the δ_(n) statistic of quantum spectra presents 1/ƒ^(α) noise. For chaotic systems α = 1 while for regular systems α = 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 α 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.