Person:
Relaño Pérez, Armando

First Name

Armando

Last Name

Relaño Pérez

URI

https://hdl.handle.net/20.500.14352/75045

Affiliation

Universidad Complutense de Madrid

Faculty / Institute

Ciencias Físicas

Department

Estructura de la Materia, Física Térmica y Electrónica

Area

Física Aplicada

Identifiers

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Now showing 1 - 10 of 60

Spectral-fluctuations test of the quark-model baryon spectrum
(Physical review letters, 2007) Fernández Ramírez, C.; Relaño Pérez, Armando
We study the low-lying baryon spectrum (up to 2.2 GeV) provided by experiments and different quark models using statistical tools which allow us to postulate the existence of missing levels in spectra. We confirm that the experimental spectrum is compatible with random matrix theory, the paradigmatic model of quantum chaos, and we find that the quark models are more similar to a Poisson distribution, which is not compatible with what should be expected in a correlated spectrum. From our analysis it stems that the spectral fluctuation properties of quark-model spectra are incompatible with experimental data. This result can be used to enlighten the problem of missing resonances.
Origin of the 1/f(alpha) spectral noise in chaotic and regular quantum systems
(Physical review E, 2018) Pachón, Leonardo A.; Relaño Pérez, Armando; Peropadre, Borja; Aspuru-Guzik, Alán
Based on the connection between the spectral form factor and the probability to return, the origin of the energy level fluctuation 1/f(alpha) noise in fully chaotic and fully integrable systems is traced to the quantum interference between invariant manifolds of the classical dynamics and the dimensionality of those invariant manifolds. This connection and the order-to-chaos transition are analyzed in terms of the statistics of Floquet's quasienergies of a classically chaotic driving nonlinear system. An immediate prediction of the connection established here is that in the presence of decoherence, the spectral exponent a takes the same value, alpha = 2, for both fully chaotic and fully integrable systems.
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 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, Aldo
Many 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.
Chaos in hadrons
(Journal of physics: Conference series, 2012) Muñoz, Laura; Fernández Ramírez, César; Relaño Pérez, Armando; Retamosa Granado, Joaquín
In the last decade quantum chaos has become a well established discipline with outreach to different fields, from condensed-matter to nuclear physics. The most important signature of quantum chaos is the statistical analysis of the energy spectrum, which distinguishes between systems with integrable and chaotic classical analogues. In recent years, spectral statistical techniques inherited from quantum chaos have been applied successfully to the baryon spectrum revealing its likely chaotic behaviour even at the lowest energies. However, the theoretical spectra present a behaviour closer to the statistics of integrable systems which makes theory and experiment statistically incompatible. The usual statement of missing resonances in the experimental spectrum when compared to the theoretical ones cannot account for the discrepancies. In this communication we report an improved analysis of the baryon spectrum, taking into account the low statistics and the error bars associated with each resonance. Our findings give a major support to the previous conclusions. Besides, analogue analyses are performed in the experimental meson spectrum, with comparison to theoretical models.
Spectral-statistics properties of the experimental and theoretical light meson spectra
(Physics Letters B, 2012) Muñoz, Laura; Fernández Ramírez, César; Relaño Pérez, Armando; Retamosa Granado, Joaquín
We present a robust analysis of the spectral fluctuations exhibited by the light meson spectrum. This analysis provides information about the degree of chaos in light mesons and may be useful to get some insight on the underlying interactions. Our analysis unveils that the statistical properties of the light meson spectrum are close, but not exactly equal, to those of chaotic systems. In addition, we have analyzed several theoretical spectra including the latest lattice QCD calculation. With a single exception, their statistical properties are close to those of a generic integrable system, and thus incompatible with the experimental spectrum.
Chaos-assisted tunneling and 1/ƒ^(α) spectral fluctuations in the order-chaos transition
(Physical review letters, 2008) Relaño Pérez, Armando
It has been shown that the spectral fluctuations of different quantum systems are characterized by 1/ƒ^(α) noise, with 1
Excited-state phase transition and onset of chaos in quantum optical models
(Physical Review E, 2011) Pérez Fernández, P.; Relaño Pérez, Armando; Arias, J. M.; Cejnar, P.; Dukelsky, J.; García Ramos, J. E.
We study the critical behavior of excited states and its relation to order and chaos in the Jaynes-Cummings and Dicke models of quantum optics. We show that both models exhibit a chain of excited-state quantum phase transitions demarcating the upper edge of the superradiant phase. For the Dicke model, the signatures of criticality in excited states are blurred by the onset of quantum chaos. We show that the emergence of quantum chaos is caused by the precursors of the excited-state quantum phase transition.
Quantum phase transitions and spontaneous symmetry-breaking in Dicke Model
(La Rabida 2012 International Scientific Meeting on Nuclear Physics: Basic Concepts in Nuclear Physics: Theory, Experiments, and Applications, 2013) Puebla, Ricardo; Relaño Pérez, Armando; Retamosa Granado, Joaquín
A method to find the Excited-States Quantum Phase Transitions (ESQPT's) from parity-symmetry in the Dicke model is studied and presented. This method allows us to stablish a critical energy where ESQPT's take places, and divides the whole energy spectrum in two regions with different properties.
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.