Person:
Gómez Gómez, José María

First Name

José María

Last Name

Gómez Gómez

URI

https://hdl.handle.net/20.500.14352/81993

Affiliation

Universidad Complutense de Madrid

Faculty / Institute

Ciencias Físicas

Area

Física Atómica, Molecular y Nuclear

Identifiers

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Now showing 1 - 10 of 12

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.
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.
Experimental evidence of chaos in the bound states of Pb-208
(Journal of Physics Conference Series, 2018) Muñoz Muñoz, Laura; Molina, R. A.; Gómez Gómez, José María; Heusler, A.
Theoretical calculations, especially shell-model calculations, have shown a strongly chaotic behavior of bound states at higher excitation energy, in regions of high level density. However, it had not been possible up to now to observe chaos in the experimental bound energy levels of any single nucleus. In this paper we study the spectral fluctuations of the Pb-208 nucleus using the complete experimental spectrum of 151 states up to excitation energies of 6.20 MeV. For natural parity states the results are very close to the predictions of Random Matrix Theory (RMT) for the nearest-neighbor spacing distribution. By contrast, the results for unnatural parity states are far from RMT behavior. We interpret these results as a consequence of the strength of the residual interaction in Pb-208, which, according to experimental data, is much stronger for natural than for unnatural parity states. In addition our results show that chaotic and non-chaotic nuclear states coexist in the same energy region of the spectrum.
Misleading signatures of quantum chaos
(Physical Review E, 2002) Gómez Gómez, José María; Molina, R. A.; Relaño Pérez, Armando; Retamosa Granado, Joaquín
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 Berry's saturation.
Stringent numerical test of the Poisson distribution for finite quantum integrable Hamiltonians
(Physical Review E, 2004) Relaño Pérez, Armando; Dukelsky, J.; Gómez Gómez, José María; Retamosa Granado, Joaquín
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.
Chaos in nuclei: Theory and experiment
(Journal of Physics Conference Series, 2018) Muñoz, L.; Molina, R. A.; Gómez Gómez, José María
During the last three decades the quest for chaos in nuclei has been quite intensive, both with theoretical calculations using nuclear models and with detailed analyses of experimental data. In this paper we outline the concept and characteristics of quantum chaos in two different approaches, the random matrix theory fluctuations and the time series fluctuations. Then we discuss the theoretical and experimental evidence of chaos in nuclei. Theoretical calculations, especially shell-model calculations, have shown a strongly chaotic behavior of bound states in regions of high level density. The analysis of experimental data has shown a strongly chaotic behavior of nuclear resonances just above the one-nucleon emission threshold. For bound states, combining experimental data of a large number of nuclei, a tendency towards chaotic motion is observed in spherical nuclei, while deformed nuclei exhibit a more regular behavior associated to the collective motion. On the other hand, it had never been possible to observe chaos in the experimental bound energy levels of any single nucleus. However, the complete experimental spectrum of the first 151 states up to excitation energies of 6.20 MeV in the Pb-208 nucleus have been recently identified and the analysis of its spectral fluctuations clearly shows the existence of chaotic motion.
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.
Correlation structure of the δ_(n) statistic for chaotic quantum systems
(Physical Review E, 2005) Relaño Pérez, Armando; Retamosa Granado, Joaquín; Faleiro, E.; Gómez Gómez, José María
The existence of a formal analogy between quantum energy spectra and discrete time series has been recently pointed out. When the energy level fluctuations are described by means of the δ_(n) statistic, it is found that chaotic quantum systems are characterized by 1/f noise, while regular systems are characterized by 1/f(2). In order to investigate the correlation structure of the δ_(n) statistic, we study the qth-order height-height correlation function C-q(tau), which measures the momentum of order q, i.e., the average qth power of the signal change after a time delay tau. It is shown that this function has a logarithmic behavior for the spectra of chaotic quantum systems, modeled by means of random matrix theory. On the other hand, since the power spectrum of chaotic energy spectra considered as time series exhibit 1/f noise, we investigate whether the qth-order height-height correlation function of other time series with 1/f noise exhibits the same properties. A time series of this kind can be generated as a linear combination of cosine functions with arbitrary phases. We find that the logarithmic behavior arises with great accuracy for time series generated with random phases.
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.
Quantum chaos and 1/f noise
(Physical review letters, 2002) Relaño Pérez, Armando; Gómez Gómez, José María; Molina, R. A.; Retamosa Granado, Joaquín; Faleiro, E.
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 Berry's saturation.