III. Ecosmos: A Revolutionary Fertile, Habitable, Solar-Bioplanet, Incubator Lifescape

E. Systems Cosmology: Fractal SpaceTimeMatter

Wei, Zong-Wen, et al. Renormalization and Small-World 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 scale-free networks. By this approach, even quantum depths can be found to contain and express the same complex, self-similar 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 one-dimensional 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 small-world transition, where a scalable quantum small-world network is achieved. Our result provides new insight into quantum repeater theory towards realistic construction of large-scale quantum networks. (Abstract)

To summarize, we have generalized one-dimensional quantum repeaters to high fractal dimension by introducing an approach called CR (coupled renormalization), which relates entanglement distribution over arbitrary fractal QRN (quantum repeater network) to recursive renormalization transformations. We assume that QRN is fractal and scale-free, which is the case for a large number of real-world networks. In spite of the large size of QRN, there exists a relatively small critical nesting level for CR, at which small-world is obtained. Small-world seems to be a necessary element for a scalable quantum network. Our study suggests that concepts and tools from statistical physics will play an important role in the joint study. It has conceived another significant direction which may open new avenue to address the outstanding issue of complexity. That is, quantum simulation of dynamic process on complex networks or design of quantum algorithms for sophisticated questions in network science. All of these attempts may dramatically alter the landscape of both fields. (5)

Weil, Melinda and Ralph Pudritz. Cosmological Evolution of Supergiant Star-Forming Clouds. The Astrophysical Journal. 556/164, 2001. Galaxies form into hierarchical clusters due to a “robust power-law mass spectrum.”

Wen, Xiao-Gang. Zoo of Quantum-Topological 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 non-zero 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 many-body 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)

New World of Condensed Matter Physics: However, through the researches in last 30 years, a different picture starts to emerge. It appears that what we have seen is just the end of beginning. There is a whole new world ahead of us waiting to be explored. A peek into the new world is offered by the discovery of fractional quantum Hall (FQH) effect. Another peek is offered by the discovery of high Tc superconductors. Both phenomena are completely beyond the paradigm of Landau’s symmetry breaking theory. Rapid and exciting developments in FQH effect and in high Tc superconductivity resulted in many new ideas and new concepts. Looking back at those new developments, it becomes more and more clear that, in last 30 years, we were actually witnessing an emergence of a new theme in condensed matter physics. The new theme is associated with new kinds of orders, new states of matter and new class of materials beyond Landau’s symmetry breaking theory. This is an exciting time for condensed matter physics. The new paradigm may even have an impact in our understanding of fundamental questions of nature – the emergence of elementary particles and the four fundamental interactions, which leads to an unification of matter and quantum information. (2)

Zhou, Yuan-Wu, 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 self-similarity 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 (MF-DFA); 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 MF-DFA 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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