### Browsing by Author "Molina, R. A."

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Publication 1/f noise and very high spectral rigidity(American Physical Society, 2006-02) Relaño Pérez, Armando; Retamosa Granado, Joaquín; Faleiro, E.; Molina, R. A.; Zuker, A. P.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.Publication 1/f noise in the two-body random ensemble(American Physical Society, 2004-07) Relaño Pérez, Armando; Molina, R. A.; Retamosa Granado, JoaquínWe show that the spectral fluctuations of the two-body random ensemble exhibit 1/f noise. This result supports a recent conjecture stating that chaotic quantum systems are characterized by 1/f noise in their energy level fluctuations. After suitable individual averaging, we also study the distribution of the exponent alpha in the 1/f(alpha) noise for the individual members of the ensemble. Almost all the exponents lie inside a narrow interval around alpha=1, suggesting that also individual members exhibit 1/f noise, provided they are individually unfolded.Publication Accuracy and precision of the estimation of the number of missing levels in chaotic spectra using long-range correlations(Springer Heidelberg, 2021-02-27) Casal, I.; Muñoz Muñoz, Laura; Molina, R. A.We study the accuracy and precision for estimating the fraction of observed levels. in quantum chaotic spectra through long-range correlations. We focus on the main statistics where theoretical formulas for the fraction of missing levels have been derived, the Delta(3) of Dyson and Mehta and the power spectrum of the delta(n) statistic. We use Monte Carlo simulations of the spectra from the diagonalization of Gaussian Orthogonal Ensemble matrices with a definite number of levels randomly taken out to fit the formulas and calculate the distribution of the estimators for different sizes of the spectrum and values of phi. A proper averaging of the power spectrum of the delta(n) statistic needs to be performed for avoiding systematic errors in the estimation. Once the proper averaging is made the estimation of the fraction of observed levels has quite good accuracy for the two methods even for the lowest dimensions we consider d = 100. However, the precision is generally better for the estimation using the power spectrum of the dn as compared to the estimation using the Delta(3) statistic. This difference is clearly bigger for larger dimensions. Our results show that a careful analysis of the value of the fit in view of the ensemble distribution of the estimations is mandatory for understanding its actual significance and give a realistic error interval.Publication Chaos and 1/f noise in nuclear spectra(World Scientific Publishing Company, 2005-03) 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.Publication Chaos in nuclei: Theory and experiment(IOP Publishing Ltd, 2018) Muñoz, L.; Molina, R. A.; Gómez Gómez, José MaríaDuring 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.Publication Comments on the dispersion relation method to vector–vector interaction(PTEP, 2019-10-21) Molina, R. A.; Geng, L S; Oset, EWe study in detail the method proposed recently to study the vector–vector interaction using the N/D method and dispersion relations, which concludes that, while, for J = 0, one finds bound states, in the case of J = 2, where the interaction is also attractive and much stronger, no bound state is found. In that work, approximations are done for N and D and a subtracted dispersion relation for D is used, with subtractions made up to a polynomial of second degree in s − sth, matching the expression to 1 − VG at threshold. We study this in detail for the ρρ interaction and to see the convergence of the method we make an extra subtraction matching 1 − VG at threshold up to (s−sth)3.We show that the method cannot be used to extrapolate the results down to 1270 MeV where the f2(1270) resonance appears, due to the artificial singularity stemming from the “on-shell” factorization of the ρ exchange potential. In addition, we explore the same method but folding this interaction with the mass distribution of the ρ, and we show that the singularity disappears and the method allows one to extrapolate to low energies, where both the (s − sth)2 and (s − sth)3 expansions lead to a zero of Re D(s), at about the same energy where a realistic approach produces a bound state. Even then, the method generates a large Im D(s) that we discuss is unphysical.Publication Decoherence induced by an interacting spin environment in the transition from integrability to chaos(American Physical Society, 2007-10) 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.Publication Examination of experimental evidence of chaos in the bound states of Pb-208(American Physical Society, 2017-01-18) Muñoz Muñoz, Laura; Molina, R. A.; Gómez, J. M. G.; Heusler, A.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 recently identified at the Maier-Leibnitz Laboratorium at Garching, Germany. For natural parity states the results are very close to the predictions of random matrix theory (RMT) for the nearest-neighbor spacing distribution. A quantitative estimate of the agreement is given by the Brody parameter omega, which takes the value omega = 0 for regular systems and omega similar or equal to 1 for chaotic systems. We obtain omega = 0.85 which is, to our knowledge, the closest value to chaos ever observed in experimental bound states of nuclei. 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 nonchaotic nuclear states coexist in the same energy region of the spectrum.Publication Experimental evidence of chaos in the bound states of Pb-208(IOP Publishing Ltd, 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.Publication Light- and strange-quark mass dependence of the ρ(770) meson revisited(Springer, 2020-11-06) Molina, R. A.; Ruiz de Elvira, J.Recent lattice data on ππ-scattering phase shifts in the vector-isovector channel, pseudoscalar meson masses and decay constants for strange-quark masses smaller or equal to the physical value allow us to study the strangeness dependence of these observables for the first time. We perform a global analysis on two kind of lattice trajectories depending on whether the sum of quark masses or the strange-quark mass is kept fixed to the physical point. The quark mass dependence of these observables is extracted from unitarized coupled-channel one-loop Chiral Perturbation Theory. This analysis guides new predictions on the ρ(770) meson properties over trajectories where the strange-quark mass is lighter than the physical mass, as well as on the SU(3) symmetric line. As a result, the light- and strange-quark mass dependence of the ρ(770) meson parameters are discussed and precise values of the Low Energy Constants present in unitarized one-loop Chiral Perturbation Theory are given. Finally, the current discrepancy between two- and three-flavor lattice results for the ρ(770) meson is studied.Publication Misleading signatures of quantum chaos(American Physical Society, 2002-09) 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.Publication Perspectives on 1/ƒ noise in quantum chaos(IOP Publishing Ltd, 2010) Relaño Pérez, Armando; Molina, R. A.; Retamosa Granado, Joaquín; Muñoz, L.; Faleiro, E.; Gómez Gómez, José MaríaThe 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.Publication Power spectrum of nuclear spectra with missing levels and mixed symmetries(Elsevier Science BV, 2007-01-04) 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.Publication Power-spectrum characterization of the continuous Gaussian ensemble(American Physical Society, 2008-03) 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).Publication Quantum chaos and 1/f noise(American Physical Society, 2002-12-09) 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.Publication Recent results in quantum chaos and its applications to atomic nuclei(IOP Publishing Ltd, 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.Publication Shell-Model studies of chaos and statistical properties in nuclei(IOP Publishing Ltd, 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.Publication Spectral statistics in noninteracting many-particle systems(American Physical Society, 2006-03) 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.Publication Spectral statistics of Hamiltonian matrices in tridiagonal form(American Physical Society, 2005-06) 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.Publication Theoretical derivation of 1/ƒ noise in quantum chaos(American Physical Society, 2004-12-10) 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.