Person:
Retamosa Granado, Joaquín

First Name

Joaquín

Last Name

Retamosa Granado

URI

https://hdl.handle.net/20.500.14352/85076

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 14

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).
Spectral statistics of Hamiltonian matrices in tridiagonal form
(Physical Review C, 2005) Relaño Pérez, Armando; Molina, R. A.; Zuker, A. P.; Retamosa Granado, Joaquín
When 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.
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.
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.
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.
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.
Thermalization in the two-body random ensemble
(Journal of statistical mechanics : theory and experiment, 2008) Kota, V. K. B.; Relaño Pérez, Armando; Retamosa Granado, Joaquín; Vyas, Manan
Using the ergodicity principle for the expectation values of several types of observables, we investigate the thermalization process in isolated fermionic systems. These are described by the two-body random ensemble, which is a paradigmatic model to study quantum chaos and especially the dynamical transition from integrability to chaos. By means of exact diagonalizations we analyze the relevance of the eigenstate thermalization hypothesis as well as the influence of other factors, such as the energy and structure of the initial state, or the dimension of the Hilbert space. We also obtain analytical expressions linking the degree of thermalization for a given observable with the so-called number of principal components for transition strengths originating at a given energy, with the dimensions of the whole Hilbert space and microcanonical energy shell, and with the correlations generated by the observable. As the strength of the residual interaction is increased, an order-to-chaos transition takes place, and we show that the onset of Wigner spectral fluctuations, which is the standard signature of chaos, is not sufficient to guarantee thermalization in finite systems. When all the signatures of chaos are fulfilled, including the quasicomplete delocalization of eigenfunctions, the eigenstate thermalization hypothesis is the mechanism responsible for the thermalization of certain types of observables, such as (linear combinations of) occupancies and strength function operators. Our results also suggest that fully chaotic systems will thermalize relative to most observables in the thermodynamic limit.
1/f noise in the two-body random ensemble
(Physical Review E, 2004) Relaño Pérez, Armando; Molina, R. A.; Retamosa Granado, Joaquín
We 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.
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.