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http://repositorio.inger.gob.mx/jspui/handle/20.500.12100/17119| Title: | Data-adaptive unfolding of nuclear excitation spectra: a time-series approach |
| metadata.dc.creator: | GAMALIEL TORRES VARGAS RUBEN YVAN MAARTEN FOSSION VICTOR MANUEL VELAZQUEZ AGUILAR JUAN CARLOS LOPEZ VIEYRA |
| Keywords: | CIENCIAS FÍSICO MATEMÁTICAS Y CIENCIAS DE LA TIERRA;Física;Física molecular;Espectroscopía molecular;Disciplinas de ciencias naturales;Física nuclear;Natural sciences disciplines;Physics;Nuclear physics;Molecular spectroscopy |
| metadata.dc.date: | 2014 |
| Publisher: | IOP Publishing |
| Description: | Abstract: A common problem in the statistical characterization of the excitation spectrum of quantum systems is the adequate separation of global system-dependent properties from the local fluctuations that are universal. In this process, called unfolding, the functional form to describe the global behaviour is often imposed externally on the data and can introduce arbitrarities in the statistical results. In this contribution, we show that a quantum excitation spectrum can readily be interpreted as a time series, before any previous unfolding. An advantage of the time-series approach is that specialized methods such as Singular Spectrum Analysis (SSA) can be used to perform the unfolding procedure in a data-adaptive way. We will show how SSA separates the components that describe the global properties from the components that describe the local fluctuations. The partial variances, associated with the fluctuations, follow a definite power law that distinguishes between soft and rigid excitation spectra. The data-adaptive fluctuation and trend components can be used to reconstruct customary fluctuation measures without ambiguities or artifacts introduced by an arbitrary unfolding, and also define the global level density of the excitation spectrum. The method is applied to nuclear shell-model calculations for 48Ca, using a realistic force and Two-Body Random Ensemble (TBRE) interactions. We show that the statistical results are very robust against a variation in the parameters of the SSA method. Conclusions: We have proposed a method to realize a data-adaptive unfolding of quantum excitation spectra, which avoids the possible ambiguities when the unfolding functional form is imposed externally to the data (e.g. using a polynomial of arbitrary degree). We interpreted the sequence of actual energy levels {E(i), i = 1 . . . N} as a generalized time series, and used the data-adaptive SSA method to separate in an unambiguous way the global trend E(i) from the local fluctuations Ee(i). This first step corresponds with the detrending part of the unfolding procedure. The statistical results are very robust against a variation in the two parameters of the method (embedding dimension L and number of trend components nT ). The partial variances, associated to the fluctuations, follow a power law that distinguishes between soft and rigid excitation spectra. If desired, the data-adaptive trend components E(i) can be used to calculate the global level density behaviour, and specialized techniques from signal analysis can be applied to the data-adaptive fluctuation components Ee(i) to further specify the fluctuation statistics. Also the rescaling step of the unfolding procedure can be carried out in a self-consistent way, after which traditional fluctuation measures such as the Nearest-Neighbour Spacing (NNS) distribution and ∆3 can be calculated without ambiguities. We tested the present data-adaptive unfolding method for the J π = 4+ excitation subspectrum of the 48Ca atomic nucleus, and our results are in correspondence with previous results in literature. This also illustrates the fact that the fluctuations in the excitation energies Ee(i) (considered in the present contribution) are statistically equivalent to the fluctuations Nf[E(i)] of the integrated density function (IDOS) (considered traditionally). In a forthcoming publication, we will show that the proposed unfolding method is general enough to apply to the excitation spectra of other quantum systems, and also to the eigenspectra of random matrices in various applications in quantum and classical physics [39]. We acknowledge financial support from CONACYT (grants CB-2011-01-167441, CB-2010-01- 155663, I010/266/2011/C-410-11 and grant 351103 from the Red Tem´atica Envejecimiento, Salud y Desarrollo Social), PAPIIT-DGAPA (grant IN114411), the European Commission (project FP7-PEOPLE-2009-IRSES-247541-MATSIQEL) and the Instituto Nacional de Geriatr´ıa (project DI-PI-002/2012). The authors wish to thank Dr. A. Frank and collaborators for fruitful discussions. |
| URI: | http://repositorio.inger.gob.mx/jspui/handle/20.500.12100/17119 |
| Appears in Collections: | 1. Artículos |
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| File | Description | Size | Format | |
|---|---|---|---|---|
| Vargas_2014_J._Phys.__Conf._Ser._492_012011.pdf | 972.9 kB | Adobe PDF | View/Open |