Criticality and long-range correlations in time series in classical and quantum systems

Landa, Emmanuel; Morales, Irving O.; Fossión, Rubén; Stránský, Pavel; Velázquez, Víctor; Vieyra, J. C. López; Frank, A.

doi:10.1103/physreve.84.016224

Cited by 24 publications

(22 citation statements)

References 42 publications

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“…We obtained a nearly 1/f power-law behavior, that is confirmed by results with α DFA = 1 for the DFA, the largest deviation being of ∼ 10% (see Table 1). These results are in agreement with the ones of Relaño et al and our previous results [24]. We also studied the energy fluctuations of the two-body random-ensemble (TBRE) [30,31] shell-model calculations for 48 Ca in the subspace J π = 0 + .…”

Section: Energy Fluctuations In Shell Model Nuclear Calculationssupporting

confidence: 91%

“…The level density is usually approximated by a smooth function (e.g. polynomial function) which can, however, affect the results, especially the sensitive long-range correlations [24]. Instead of following this procedure, in this paper we employ the Empirical Mode Decomposition (EMD) method to perform the unfolding procedure in quantum excitation spectra.…”

Section: Module-1 Logistic Mapmentioning

confidence: 99%

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Scale Invariance, Self Similarity and Critical Behavior in Classical and Quantum Systems

Morales¹,

Landa²,

Fossión³

et al. 2012

J. Phys.: Conf. Ser.

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Abstract. Symmetry and self-affinity or scale invariance are related concepts. We explore the fractal properties of fluctuations in dynamical systems, using some of the available tools in the context of time series analysis. We carry out a power spectrum study in the Fourier domain, the method of detrended fluctuation analysis and the investigation of autocorrelation function behavior. Our study focuses on two particular examples, the logistic module-1 map, which displays properties of classical dynamical systems, and the excitation spectrum of a schematic shell-model Hamiltonian, which is a simple system exhibiting quantum chaos.

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Section: Energy Fluctuations In Shell Model Nuclear Calculationssupporting

confidence: 91%

Section: Module-1 Logistic Mapmentioning

confidence: 99%

Scale Invariance, Self Similarity and Critical Behavior in Classical and Quantum Systems

Morales¹,

Landa²,

Fossión³

et al. 2012

J. Phys.: Conf. Ser.

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“…Hence, time series with interactions such that χ > 0.1, still possess a certain degree of coherence. In this case, the 1/f noise, characteristic of nuclear spectrum [14,15,16,17,10], corresponds to the same fluctuations found in the analysis of the eigenvalues of random matrices [18,19,20] of a two-body random ensemble (TBRE). Studies of these random matrices showed that nuclear energy levels of low-energy excited states of complex nuclei follow a complete statistics, and not a random one.…”

Section: Power Spectrum and Visibilitysupporting

confidence: 53%

“…1) we can obtain the energy time series of the fluctuations. In [10,11] the method of power spectrum analysis (PS) [14,15,16,17] is used to study the statistical of fluctuations of energy time series. Following the 1/f β noise convention, three of the most conventional noises present in nature are for β = 2, 1, 0 corresponding to thermal (Brownian), chaotic and Poisson noise respectively [12].…”

Section: Power Spectrum and Visibilitymentioning

confidence: 99%

Quantum interference vs. quantum chaos in the nuclear shell model

Fernández

Hernández

Hautefeuille

et al. 2015

J. Phys.: Conf. Ser.

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Abstract. In this paper we study the complexity of the nuclear states in terms of a two body quadupole-quadrupole interaction. Energy distributions and eigenvectors composition exhibit a visible interference pattern which is dependent on the intensity of the interaction. In analogy with optics, the visibility of the interference is related to the purity of the states, therefore, we show that the fluctuations associated with quantum chaos have as their origin the remaining quantum coherence with a visibility magnitude close to 5%.

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“…In a recent approach, the unfolded fluctuations of the accumulated level density function N (E) = N (E) − N (E) (also called δ n function) * Email: fossion@nucleares.unam.mx were interpreted as a time series [4,20,21]. This treatment opened the field to the application of specialized techniques from signal analysis, such as Fourier spectral analysis [4,7,20,21], Detrended Fluctuation Analysis (DFA) [22][23][24], wavelets [25], Empirical Mode Decomposition (EMD) [26][27][28], and normal-mode analysis [29,30]. The result of these investigations is that for Gaussian RMT ensembles, the fluctuation time series is scale invariant (fractal), which in the Fourier power spectrum is reflected in a power law,…”

mentioning

confidence: 99%

Random-matrix spectra as a time series

2013

Self Cite

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Spectra of ordered eigenvalues of finite Random Matrices are interpreted as a time series. Dataadaptive techniques from signal analysis are applied to decompose the spectrum in clearly differentiated trend and fluctuation modes, avoiding possible artifacts introduced by standard unfolding techniques. The fluctuation modes are scale invariant and follow different power laws for Poisson and Gaussian ensembles, which already during the unfolding allows to distinguish the two cases.PACS numbers: 05.45. Tp,05.45.Mt,02.50.Sk The study of spectral fluctuations within the framework of Random Matrix Theory (RMT) is a standard tool in the statistical study of quantum chaos in the excitation spectra of quantum systems [1][2][3][4]. Recently, the approach has found new applications in many fields, such as in the study of eigenspectra of adjacency matrices of networks [5][6][7], and eigenspectra of empirical correlation matrices in finance [8][9][10], the climate [11], electro-and magnetoencephalography [12][13][14], and in complex systems [15]. The interest of the approach lies in the fact that the level density fluctuations ρ(E) = ρ(E) − ρ(E) around the smooth global density ρ(E) are universal and indicate the underlying symmetry class of the system [2,16]. On the other hand, the global level density ρ(E) is system dependent, and an unfolding procedure needs to be performed, to separate the global and the fluctuating parts [1]. The unfolding is straightforward if an analytical formula is known to describe the global level density ρ(E) for the system under study, such as e.g. the gaussian and semicircle distributions for Possion and GOE matrix ensembles from RMT [2], or the MarchenkoPastur distribution for the Laguerre ensemble of random Wishart correlation matrices [17]. However, such analytical formulae are formally only adequate in the asymptotic limit for spectra with an infinite number of levels. Often, an analytical form for ρ(E) is unknown, as is the case for adjacency matrices [5]. In practical cases, having finite, albeit large matrices, the usual approach is then to project the sequence of ordered eigenvalues into unfolded values E(n) → N [E(n)], using a smooth (often polynomial) approximation N (E) to the accumulated density , 5, 20]. After unfolding, the short-range and long-range correlations can be quantified using standard fluctuations measures such as the Nearest-Neighbour Spacing (NNS) distribution, number variance Σ 2 and ∆ 3 . In a recent approach, the unfolded fluctuations of the accumulated level density function N (E) = N (E) − N (E) (also called δ n function) *

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Criticality and long-range correlations in time series in classical and quantum systems

Cited by 24 publications

References 42 publications

Scale Invariance, Self Similarity and Critical Behavior in Classical and Quantum Systems

Scale Invariance, Self Similarity and Critical Behavior in Classical and Quantum Systems

Quantum interference vs. quantum chaos in the nuclear shell model

Random-matrix spectra as a time series

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