arXiv subjects

J. M. G. Gomez

Publications and source records attributed to J. M. G. Gomez.

8 recordsLinked to original sources

arXiv2005

$1/f^α$ Noise in Spectral Fluctuations of Quantum Systems

The power law $1/f^α$ 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 fluctuations can be characterized by the power spectrum. Using a family of quantum billiards, we analyze the order to chaos transition in terms of this power spectrum. A power law $1/f^α$ is found at all the transition stages, and it is shown that the exponent $α$ is related to the chaotic component of the classical phase space of the quantum system.

cond-mat.stat-mech↗

arXiv2004

Stringent Numerical Test of the Poisson Distribution for Finite Quantum Integrable Hamiltonians

Using a new 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 cases, 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 to the work of the Berry and Tabor in the semiclassical limit.

nlin.CD↗

arXiv2001

Misleading signatures of quantum chaos

The main signature of chaos in a quantum system is provided by spectral statistical analysis of the nearest neighbor spacing distribution and the spectral rigidity given by $Δ_3(L)$. It is shown that some standard unfolding procedures, like local unfolding and Gaussian broadening, lead to a spurious increase of the spectral rigidity that spoils the $Δ_3(L)$ relationship with the regular or chaotic motion of the system. This effect can also be misinterpreted as Berry's saturation.

nlin.CD↗

arXiv2000

Transition Strength Sums and Quantum Chaos in Shell Model States

For the embedded Gaussian orthogonal ensemble (EGOE) of random matrices, the strength sums generated by a transition operator acting on an eigenstate vary with the excitation energy as the ratio of two Gaussians. This general result is compared to exact shell model calculations, with realistic interactions, of spherical orbit occupancies and Gamow-Teller strength sums in some $(ds)$ and $(fp)$ shell examples. In order to confirm that EGOE operates in the chaotic domain of the shell model spectrum, calculations are carried out using two different interpolating hamiltonians generating order-chaos transitions. Good agreement is obtained in the chaotic domain of the spectrum, and strong deviations are observed as nuclear motion approaches a regular regime (transition strength sums appear to follow the Dyson's $Δ_3$ statistic). More importantly, they shed new light on the newly emerging understanding that in the chaotic domain of isolated finite interacting many particle systems smoothed densities (they include strength functions) define the statistical description of these systems and these densities follow from embedded random matrix ensembles; some EGOE calculations to this end are presented.

nucl-th↗

arXiv1998

Large Shell Model Calculations for Calcium Isotopes: Spectral Statistics and Chaos

We perform large shell model calculations for Calcium isotopes in the full fp shell by using the realistic Kuo-Brown interaction. The Calcium isotopes are especially interesting because the nearest-neighbour spacing distribution P(s) of low-lying energy levels shows significant deviations from the predictions of the Gaussian Orthogonal Ensemble of random--matrix theory. This contrasts with other neighbouring nuclei which show fully chaotic spectral distributions. We study the chaotic behaviour as a function of the excitation energy. In addition, a clear signature of chaos suppression is obtained when the single-particle spacings are increased. In our opinion the relatively weak strength of the neutron-neutron interaction is unable to destroy the regular single-particle mean-field motion completely. In the neighbouring nuclei with both protons and neutrons in valence orbits, on the other hand, the stronger proton-neutron interaction would appear to be sufficient to destroy the regular mean-field motion.

nucl-th↗

arXiv1997

Spectral Distribution Studies of fp shell nuclei with modified Kuo--Brown Interaction

The structure of nuclei in the lower half of fp shell is investigated by the spectral distribution method using the modified Kuo-Brown interaction. This interaction recently showed success in reproducing observed properties through detailed shell model studies. Spectral distribution studies avoid explicit diagonalization and hold promise for applications to astrophysics.

nucl-th↗

arXiv1995

Quantum Chaos in A=46--50 Atomic Nuclei

The spectral statistics of low--lying states of several $fp$ shell nuclei are studied with realistic shell--model calculations. For Ca isotopes, we find significant deviations from the predictions of the random--matrix theory which suggest that some spherical nuclei are not as chaotic in nature as the conventional view assumes.

nucl-th↗

arXiv1995

Spectral Statistics in Large Shell Model Calculations

The spectral statistics of low--lying states of $fp$ shell nuclei are studied by performing large shell--model calculations with a realistic nuclear interaction. For $Ca$ isotopes, we find deviations from the predictions of the random--matrix theory which suggest that some spherical nuclei are not as chaotic in nature as the conventional view assumes.

nucl-th↗