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Relaño Pérez, Armando ; Retamosa Granado, Joaquín ; Faleiro, E. ; Molina, R. A. ; Zuker, A. P. | American Physical Society | 2006-02It 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 [...]texto impreso
Relaño Pérez, Armando ; Molina, R. A. ; Retamosa Granado, Joaquín | American Physical Society | 2004-07We 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 suit[...]texto impreso
Relaño Pérez, Armando ; Gómez Gómez, José María ; Retamosa Granado, Joaquín ; Faleiro, E. ; Salasnich, L. ; Vranicar, M. ; Robnik, M. | American Physical Society | 2005-03-04The power law 1/ƒ^(?) in the power spectrum characterizes the fluctuating observables of many complex natural systems. Considering the energy levels of a quantum system as a discrete time series where the energy plays the role of time, the level[...]texto impreso
Muñoz, Laura ; Fernández Ramírez, César ; Relaño Pérez, Armando ; Retamosa Granado, Joaquín | IOP publishing ltd | 2012In 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 spectr[...]texto impreso
Relaño Pérez, Armando ; Retamosa Granado, Joaquín ; Faleiro, E. ; Gómez Gómez, José María | American Physical Society | 2005-12The 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 ?_(n) statistic, it is found that chaotic quantum systems a[...]texto impreso
Puebla, Ricardo ; Relaño Pérez, Armando ; Retamosa Granado, Joaquín | American Physical Society | 2013-02-19We study the phase diagram of the Dicke model in terms of the excitation energy and the radiation-matter coupling constant lambda. Below a certain critical value lambda(c), all the energy levels have a well-defined parity. For lambda > lambda(c[...]texto impreso
Gómez Gómez, José María ; Molina, R. A. ; Relaño Pérez, Armando ; Retamosa Granado, Joaquín | American Physical Society | 2002-09The 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[...]texto impreso
Relaño Pérez, Armando ; Molina, R. A. ; Retamosa Granado, Joaquín ; Muñoz, L. ; Faleiro, E. ; Gómez Gómez, José María | IOP publishing ltd | 2010The power spectrum of the ?_(n) statistic of quantum spectra presents 1/ƒ^(?) noise. For chaotic systems ? = 1 while for regular systems ? = 2. Although the transition from regularity to chaos is non universal, for a wide variety of systems wi[...]texto impreso
Relaño Pérez, Armando ; Muñoz, L. ; Retamosa Granado, Joaquín ; Faleiro, E. ; Molina, R. A. | American Physical Society | 2008-03The 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 p[...]texto impreso
Relaño Pérez, Armando ; Molina, R. A. ; Retamosa Granado, Joaquín ; Muñoz, L. ; Faleiro, E. | Elsevier Science BV | 2007-01-04Sequences 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 diffe[...]texto impreso
Faleiro, E. ; Gómez Gómez, José María ; Muñoz, L. ; Relaño Pérez, Armando ; Retamosa Granado, Joaquín | University Chicago Press | 2004-11We 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 r[...]texto impreso
Relaño Pérez, Armando ; Gómez Gómez, José María ; Molina, R. A. ; Retamosa Granado, Joaquín ; Faleiro, E. | American Physical Society | 2002-12-09The 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[...]texto impreso
Puebla, Ricardo ; Relaño Pérez, Armando ; Retamosa Granado, Joaquín | American Institute of Physics (AIP) | 2013A 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[...]texto impreso
Relaño Pérez, Armando ; Muñoz, L. ; Faleiro, E. ; Molina, R. A. ; Retamosa Granado, Joaquín | American Physical Society | 2006-03It 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 hav[...]texto impreso
Relaño Pérez, Armando ; Molina, R. A. ; Zuker, A. P. ; Retamosa Granado, Joaquín | American Physical Society | 2005-06When 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 [...]
