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Scale invariance, self similarity and critical behavior in classical and quantum systems

dc.rights.licensehttp://creativecommons.org/licenses/by/4.0es_MX
dc.creatorIRVING OMAR MORALES AGISSes_MX
dc.creatorEMMANUEL LANDA HERNANDEZes_MX
dc.creatorRUBEN YVAN MAARTEN FOSSIONes_MX
dc.creatorALEJANDRO FRANK HOEFLICHes_MX
dc.date2012
dc.date.accessioned2018-10-23T20:16:58Z
dc.date.available2018-10-23T20:16:58Z
dc.identifier.urihttp://repositorio.inger.gob.mx/jspui/handle/20.500.12100/17107
dc.descriptionAbstract: Symmetry and self-affinity or scale invariance are related concepts. We explore the fractal properties of fluctuations in dynamical systems, using some of the available tools in the context of time series analysis. We carry out a power spectrum study in the Fourier domain, the method of detrended fluctuation analysis and the investigation of autocorrelation function behavior. Our study focuses on two particular examples, the logistic module-1 map, which displays properties of classical dynamical systems, and the excitation spectrum of a schematic shell-model Hamiltonian, which is a simple system exhibiting quantum chaos.es_MX
dc.descriptionConclusions: Self-similarity is a very important property of dynamical systems which can be analyzed usingthe usual tools of time-series analysis. For the dynamical systems presenting scale invariancethe power spectral density behaves as a power lawP(f)∼1/fβ. The 1/fnoise (β= 1) can beseen as a particular type of self-similar noise. It corresponds to signals that maximize the rangeof their correlations. We suggest in this paper that time series of both classical and quantumdynamical systems that undergo a transition between two regimes, exhibit 1/fbehavior nearthe transitional point. We report in detail on two specific examples: the Module-1 Logistic Mapfor the classical case, and a schematic nuclear shell-model Hamiltonian for the quantum case.We studied the corresponding time series by spectral analysis, and with the DFA method.In the case of the module-1 logistic map, for values of the control parameterk <0, wefound regular time series (with Lyapunov exponentλk<0), for a value ofk= 1, a correlated non-periodic time series (with Lyapunov exponentλk= 0), and for control parametersk >1we observe chaotic time series (with Lyapunov exponentλk>0). We find 1/fbehavior for thecorrelated non-periodic time series at the transitional point, whereas the regular and chaotictime series correspond to 1/fβ(β6= 1) power spectral density. We describe a generic nuclear ex-citation spectrum, using a schematic Hamiltonian. The Hamiltonian has two competing terms:a single-particle term, and a residual quadrupole-quadrupole term. Each term individually isintegrable. A control parameter allows for a smooth transition between the two extreme regimes.Both extreme integrable excitation spectra correspond to 1/f2(brownian) power laws, whereasthe transitional excitation spectrum corresponds with a 1/fpower spectral density. For twospecific systems, we found a generic 1/fbehavior of the corresponding time series, where thelong-range correlations are maximized, exactly at the point where the transition occurs. Weare currently applying these techniques to other systems, such as simple coupled pendula andphoton counting rates in different kinds of emitting light sources [34]. We believe that time se-ries analysis can provide relevant information in both physical and biological systems, includingearly warning signals in diverse phenomena.es_MX
dc.formatAdobe PDFes_MX
dc.languageenges_MX
dc.publisherIOP Sciencees_MX
dc.relationhttp://iopscience.iop.org/article/10.1088/1742-6596/380/1/012020es_MX
dc.relation.requiresSies_MX
dc.rightsopenAccesses_MX
dc.sourceJournal of Physics: Conference Series (1742-6596) vol. 380 (2012)es_MX
dc.subjectCIENCIAS FÍSICO MATEMÁTICAS Y CIENCIAS DE LA TIERRAes_MX
dc.subjectFísicaes_MX
dc.subjectFísica teóricaes_MX
dc.subjectTeoría cuántica de camposes_MX
dc.subjectFísica nucleares_MX
dc.subjectPhysicses_MX
dc.subjectNuclear physicses_MX
dc.subjectQuantum theoryes_MX
dc.titleScale invariance, self similarity and critical behavior in classical and quantum systemses_MX
dc.typearticlees_MX
dc.audienceResearcherses_MX
dc.creator.idMOAI810829HDFRGR00es_MX
dc.creator.idLAHE840702HVZNRM02es_MX
dc.creator.idFORU771115HNESXB09es_MX
dc.creator.idFAHA510804HNLRFL05es_MX
dc.creator.nameIdentifiercurpes_MX
dc.creator.nameIdentifiercurpes_MX
dc.creator.nameIdentifiercurpes_MX
dc.creator.nameIdentifiercurpes_MX


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