Scale invariance and criticality in nuclear spectra

E. Landa^ª, I. Moralesª, C. Hernándezª, J.C. López Vieyraª, A. Frankª, and V. Velázquez^b

ª Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, Apartado Postal 70–543, México, D.F. 04510 México.

^b Facultad de Ciencias, Universidad Nacional Autónoma de México, México, D.F. 04510 México.

Recibido el 15 de abril de 2008
Aceptado el 9 de mayo de 2008

Abstract

A Detrended Fluctuation Analysis (DFA) method is applied to investigate the scaling properties of the energy fluctuations in the spectrum of ⁴⁸Ca obtained with (a) a large realistic shell model calculation (ANTOINE code) and (b) with a random shell model (TBRE) calculation. We compare the scale invariant properties of the energy fluctuations with similar analyses applied to the RMT ensembles GOE and GDE. A comparison with the related power spectra calculations is made. The possible consequences of these results are discussed.

Keywords: Quantum chaos; scale invariance; TBRE; DFA.

Resumen

Se aplica el método DFA (Detrended Fluctuation Analysis) para investigar las propiedades de escalamiento de las fluctuaciones de la energía en el espectro del ⁴⁸Ca obtenido con (a) un cálculo del modelo de capas realista (codigo ANTOINE) y con (b) un cálculo del modelo de capas aleatorio (TBRE). Comparamos las propiedades invariantes de escala de las fluctuaciones de energía con analisis similares aplicados a ensembles GOE y GDE de la teoría de matrices aleatorias (RMT). Se hace una comparación con cálculos relacionados de espectro de potencias. Se discute las posibles consecuencias de esos resultados.

Descriptores: Caos cuántico; invariancia de escala; TBRE; DFA.

PACS:05.45.Mt;24.60.Lz;52.25.Gj;74.40.+k;89.75.Da

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Acknowledgments

We are grateful to Jose Barea for his many suggestions. We thank H. Larralde for his valuable comments. This work was supported in part by PAPIIT–UNAM and Conacyt–México.

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