Person: Relaño Pérez, Armando
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First Name
Armando
Last Name
Relaño Pérez
Affiliation
Universidad Complutense de Madrid
Faculty / Institute
Ciencias Físicas
Department
Estructura de la Materia, Física Térmica y Electrónica
Area
Física Aplicada
Identifiers
14 results
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Now showing 1 - 10 of 14
Item 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, AldoMany 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.Item Decoherence induced by an interacting spin environment in the transition from integrability to chaos(Physical Review E, 2007) Relaño Pérez, Armando; Dukelsky, J.; Molina, R. A.We investigate the decoherence properties of a central system composed of two spins 1/2 in contact with a spin bath. The dynamical regime of the bath ranges from a fully integrable limit to complete chaoticity. We show that the dynamical regime of the bath determines the efficiency of the decoherence process. For perturbative regimes, the integrable limit provides stronger decoherence, while in the strong coupling regime the chaotic limit becomes more efficient. We also show that the decoherence time behaves in a similar way. On the contrary, the rate of decay of magnitudes like linear entropy or fidelity does not depend on the dynamical regime of the bath. We interpret the latter results as due to a comparable complexity of the Hamiltonian for both the integrable and the fully chaotic limits.Item Misleading signatures of quantum chaos(Physical Review E, 2002) Gómez Gómez, José María; Molina, R. A.; Relaño Pérez, Armando; Retamosa Granado, JoaquínThe 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 Berry's saturation.Item 1/f noise and very high spectral rigidity(Physical Review E, 2006) Relaño Pérez, Armando; Retamosa Granado, Joaquín; Faleiro, E.; Molina, R. A.; Zuker, A. P.Abstract: It was recently pointed out that the spectral fluctuations of quantum systems are formally analogous to discrete time series, and therefore their structure can be characterized by the power spectrum of the signal. Moreover, it is found that the power spectrum of chaotic spectra displays a 1/f behavior, while that of regular systems follows a 1/f(2) law. This analogy provides a link between the concepts of spectral rigidity and antipersistence. Trying to get a deeper understanding of this relationship, we have studied the correlation structure of spectra with high spectral rigidity. Using an appropriate family of random Hamiltonians, we increase the spectral rigidity up to hindering completely the spectral fluctuations. Analyzing the long range correlation structure a neat power law 1/f has been found for all the spectra, along the whole process. Therefore, 1/f noise is the characteristic fingerprint of a transition that, preserving the scale-free correlation structure, hinders completely the fluctuations of the spectrum.Item Spectral statistics in noninteracting many-particle systems(Physical Review E, 2006) Relaño Pérez, Armando; Muñoz, L.; Faleiro, E.; Molina, R. A.; Retamosa Granado, JoaquínIt 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.Item 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).Item 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, JoaquínIt 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.Item 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, ArmandoShell-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.Item 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.Item Spectral statistics of Hamiltonian matrices in tridiagonal form(Physical Review C, 2005) Relaño Pérez, Armando; Molina, R. A.; Zuker, A. P.; Retamosa Granado, JoaquínWhen a matrix is reduced to Lanczos tridiagonal form, its matrix elements can be divided into an analytic smooth mean value and a fluctuating part. The next-neighbor spacing distribution P(s) and the spectral rigidity Delta _(3) are shown to be universal functions of the average value of the fluctuating part. It is explained why the behavior of these quantities suggested by random matrix theory is valid in far more general cases.