
III. An Organic, Conducive, Habitable MultiUniVerseF. Systems Cosmology: Fractal SpaceTimeMatter Vijar, Sagar, et al. A New Kind of Topological Quantum Order. arXiv:1505.02576. With a Dimensional Hierarchy of Quasiparticles Built from Stationary Excitations subtitle, by way of clever mathematics, MIT physicists SV, Jeongwan Haah, and Liang Fu advance deep understandings about how cosmic nature’s is actually suffused by intrinsic structural geometries. See also Haah’s 2011 original paper Local Stabilizer Codes in Three Dimensions without String Logical Operators at 1101.1962 with much set off this quest. We introduce exactly solvable models of interacting (Majorana) fermions in d≥3 spatial dimensions that realize a new kind of topological quantum order, building on a model presented in ref. [1]. These models have extensive topological groundstate degeneracy and a hierarchy of pointlike, topological excitations that are only free to move within submanifolds of the lattice. In particular, one of our models has fundamental excitations that are completely stationary. To demonstrate these results, we introduce a powerful polynomial representation of commuting Majorana Hamiltonians. Remarkably, the physical properties of the topologicallyordered state are encoded in an algebraic variety, defined by the common zeros of a set of polynomials over a finite field. This provides a "geometric" framework for the emergence of topological order. (Abstract) Von Korff, Modest and Thomas Sander. Molecular Complexity Calculated by Fractal Dimension. Nature Scientific Reports. 9/967, 2019. Scientific Computing Drug Discovery, Idorsia Pharmaceuticals, Switzerland researchers achieve another novel recognition that nature’s proclivity to adopt and display a selfsimilar, iterative essence can be traced even to molecular and atomic forms and substructures. Molecular complexity is an important characteristic of organic molecules for drug discovery. How to calculate molecular complexity has been discussed in the scientific literature for decades. It was known from early on that the numbers of substructures that can be cut out of a molecular graph are of importance. However, it was never realized that the cutout substructures show selfsimilarity to the parent structures. Such a series shows selfsimilarity similar to fractal objects. The fractal dimension of a molecule is a new matter constant that incorporates all features that are currently known to be important for describing molecular complexity.(Abstract) Vrobel, Susie, et al, eds. Simultaneity: Temporal Structures and Observer Perspectives. Hackensack, NJ: World Scientific, 2008. With coeditors Otto Rossler and Terry MarksTarlow, a volume emanating from an Institute for Fractal Research which seems to get wound up in its own vernacular claiming “the next revolution in physics” due to novel appreciations of human observership and the inherent “fractality of space and time.” An eclectic collection, with various contributions by the editors, Peter Allen on a hierarchy of evolutionary systems, Uri Fidelman on complementary brain hemispheres whereof the right side achieves its simultaneous synthesis, and on to a brush with econophysics. In any event, still another sign of coming universe change. Walcher,, C. J., et al. SelfSimilarity in the Chemical Evolution of Galaxies. arXiv:1607.00015. A ten person team from Germany and South America report signs of a universal geometric repetition across material, stellar and galactic realms that is “more than just a coincidence.” Recent improvements in the age dating of stellar populations and single stars allow us to study the ages and abundance of stars and galaxies with unprecedented accuracy. We here compare the relation between age and \alphaelement abundances for stars in the solar neighborhood to that of local, earlytype galaxies. This quantitative similarity seems surprising, given the different types of galaxies and scales involved. The data are consistent with a power law delay time distribution. We thus confirm that the delay time distribution inferred for the Milky Way from chemical evolution arguments also must apply to massive earlytype galaxies. Wang, Xin and Alex Szalay. On the Nonlinear Evolution of Cosmic Web. arXiv.1411.4117. Johns Hopkins University astrophysicists explain “cosmic morphologies of the largestructure” by way of Lagrangian dynamics, a technical finesse of statistical mechanics. We cite because by natural philosophy wonder, how fantastic is it that human folks can altogether suddenly traverse and quantify such infinite vistas. You might read Johns Hopkins (17951873) biography on Wikipedia for some context. Surely we peoples ought to grant ourselves a central significance to the course and fate of this genesis universe. Wang, Yi and Robert Brandenberger. ScaleInvariant Fluctuations from Galilean Genesis. arXiv:1007.0027. Posted June 2012, McGill University physicists take up the work of Paolo Creminelli, et al, Abdus Salam International Centre for Theoretical Physics, posted October 2010 (search arXiv) to glean further insights upon a fractal cosmos. We include both Abstracts. “Inflation on Trial” by Alexandra Witze in Science News for July 25, 2012 reports on these 21st century revisions of the 1980s and 1990s instant inflation theories. We study the spectrum of cosmological fluctuations in scenarios such as Galilean Genesis in which a spectator scalar field acquires a scaleinvariant spectrum of perturbations during an early phase which asymptotes in the far past to Minkowski spacetime. In the case of minimal coupling to gravity and standard scalar field Lagrangian, the induced curvature fluctuations depend quadratically on the spectator field and are hence nonscaleinvariant and highly nonGaussian. We show that if higher dimensional operators are considered, a linear coupling between background and spectator field fluctuations is induced which leads to scaleinvariant and Gaussian curvature fluctuations. (Wang, Brandenberger) Watkins, Nicholas, et al. 25 Years of SelfOrganized Criticality. Space Science Reviews. Online Summer, 2015. The document is also at arXiv:1504.04991. It is a consummate paper to be published in a special retrospective issue along with Marcus Aschwanden, et al, 25 Years of SOC: Space and Laboratory Plasmas (search), James McAteer, et al, 25 Years of SOC: Numerical Detection, and other articles. As the Aschwanden posting explains, the once and future review stems from a series of International Space Science Institute workshops. In accord with a 2015 emergent synthesis of constant work and progress since the 1980s, across these widest natural domains is affirmed a robust “ubiquity, universality, generality” (26). See also a commentary on the work SOC Revisited by Mark Buchanan in Nature Physics for June 2015. Introduced by the late Per Bak and his colleagues, selforganized criticality (SOC) has been one of the most stimulating concepts to come out of statistical mechanics and condensed matter theory in the last few decades, and has played a significant role in the development of complexity science. SOC, and more generally fractals and power laws, have attracted much comment, ranging from the very positive to the polemical. The other papers in this special issue showcase the considerable body of observations in solar, magnetospheric and fusion plasma inspired by the SOC idea, and expose the fertile role the new paradigm has played in approaches to modeling and understanding multiscale plasma instabilities. This very broad impact, and the necessary process of adapting a scientific hypothesis to the conditions of a given physical system, has meant that SOC as studied in these fields has sometimes differed significantly from the definition originally given by its creators. One aim of the present review is to address the dichotomy between the great reception SOC has received in some areas, and its shortcomings, as they became manifest in the controversies it triggered. Our article tries to clear up what we think are misunderstandings of SOC in fields more remote from its origins in statistical mechanics, condensed matter and dynamical systems by revisiting Bak, Tang and Wiesenfeld's original papers. (Abstract) Wei, ZongWen, et al. Renormalization and SmallWorld Model of Fractal Quantum Repeater Networks. Nature Scientific Reports. 3/1222, 2013. Hangzhou Normal University, and University of Science and Technology of China, system physicists achieve a number of syntheses in this innovative paper. Traditional statistical mechanics is melded with nonlinear science to join renormalization theories with dynamic scalefree networks. By this approach, even quantum depths can be found to contain and express the same complex, selfsimilar system phenomena as everywhere else in nature and society. Such a novel, holistic vista can even more reveal and implicate, albeit in arcane terms than beg translation, an independent, creative, universal source. Quantum networks provide access to exchange of quantum information. The primary task of quantum networks is to distribute entanglement between remote nodes. Although quantum repeater protocol enables long distance entanglement distribution, it has been restricted to onedimensional linear network. Here we develop a general framework that allows application of quantum repeater protocol to arbitrary quantum repeater networks with fractal structure. Entanglement distribution across such networks is mapped to renormalization. Furthermore, we demonstrate that logarithmical times of recursive such renormalization transformations can trigger fractal to smallworld transition, where a scalable quantum smallworld network is achieved. Our result provides new insight into quantum repeater theory towards realistic construction of largescale quantum networks. (Abstract) Weil, Melinda and Ralph Pudritz. Cosmological Evolution of Supergiant StarForming Clouds. The Astrophysical Journal. 556/164, 2001. Galaxies form into hierarchical clusters due to a “robust powerlaw mass spectrum.” Wen, XiaoGang. Zoo of QuantumTopological Phases of Matter. arXiv:1610.03911. The MIT physicist and author has engaged this field for some years (check his publications page) and was interviewed by Natalie Wolchover for her 2018 Quanta report above which displays a “Periodic Table of Phases” that Wen conceived. This paper advances the 2010s turn in condensed matter physics from material and energetic aspects to realize that nature’s quantum realm is equally distinguished by innate geometric formations, which seem to arrange in an orderly way. We quote a full paragraph to convey its content. What are topological phases of matter? First, they are phases of matter at zero temperature. Second, they have a nonzero energy gap for the excitations above the ground state. Third, they are disordered liquids that seem have no feature. But those disordered liquids actually can have rich patterns of manybody entanglement representing new kinds of order. This paper will give a simple introduction and a brief survey of topological phases of matter. We will first discuss topological phases that have topological order (ie with long range entanglement). Then we will cover topological phases that have no topological order. (Abstract) Zhou, YuanWu, et al. Multifractal and Complex Network Analyses of Protein Molecular Dynamics. arXiv:1403.4719. As the Abstract excerpts note, Xiangtan University, Hunan, and Queens University of Technology, Brisbane, researchers find nature’s universal selfsimilarity to be equally present in this vital class of intricate biomolecules. Based on protein molecular dynamics, we analyze fractal properties of energy, pressure and volume time series using the multifractal detrended fluctuations analysis (MFDFA); and investigate the topological and multifractal properties of their visibility graph (complex network) representations. The energy terms of proteins we considered are bonded potential, angle potential, dihedral potential, improper potential, kinetic energy, Van der Waals potential, electrostatic potential, total energy and potential energy. Results of MFDFA show that these time series are multifractal. Results of complex networks analysis based on visibility graph algorithm show that these visibility graphs are exponential. Our numerical results of multifractal analysis of the visibility graphs show that multifractality exists in these networks. (Abstract)
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