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Toward a Dynamics of Emergence - On the long way I walked along with Professor Zhuo - Fumihiko Sakata Professor Emeritus, Ibaraki University Member of the board of directors, Gushinkai Foundation Talk presented at China Institute of Atomic Energy, Oct. 19, 2011

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Introduction Theory of large-amplitude collective motion(Maskawa 1980) Microscopic origin of nuclear dissipation Nuclear Coupled Master Equation (Zhuo 1989) Microscopic theory of order-to-chaos transition in nuclei (Nonlinear Dynamics) Dynamical origin of stationary statistical state in finite system (Wu, Li,1996 Yan ) Quantum Chaos, quantum non-linear resonance, … Level crossing dynamics (Guo 2005) important for nuclear fusion, fission, HI-DIC,… new property could not be predicted from a knowledge of the lower-level properties the whole is greater than the composition of its parts emergence is specific for biological (living) system, complex system, self- organizing system, system of network, … Finite, self-sustained, Strongly interacting, nonlinear complex system Emergence Nucleus to derive a transport equation

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Non-linear Dynamics in Chemical Reaction Order-to-Chaos Dynamics, Non-linear Resonance, Quantum Chaos might play role in nuclear fission & fusion process A. Bohr Transition state Chemical Reaction https://www.cps-jp.org/~21coeps/pub /POSTER//POSTER/PDF/sg03-Cross-Talk.pdf nuclear fission process Poincare section map of standard map Transition state theory Henry Eyring, JCP3(1935)107

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Micro-level Dynamics Described by Schrödinger Eq. for Constituent Particles Microscopic Numerical Simulation Ab-initio (GF Monte Carlo), Configulation Interaction, density functional Theory Reduction Principle of dof Projection Operator Method Coarse-Graining Procedure Memory Effects Scale Separation Dynamics of Protein Folding and conformation J. Am. Chem. Soc., 2010, 132 (38), Macro-level Dynamics described by Fluid Dynamics, Transport Eq. Langevin Eq. Fokker-Planck Eq. Hill-Wheeler1953 A. Bohr Transition state order-to-chaos transition plays an important role Science in the Era of High Performance Computer

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Microscopic Equation High- Performance Computer Experiment Black Box Treasure Box Emergence of Macro-Dynamics out of Micro-Dynamics Dynamics of Emergence should describe Change of Nuclear Structure as well as Reaction Process There are no unified theory of reactions between two complex system two body scatteringsuperposition of nn-scattering What happens in between ? Impulse DWBA Eikonal Coupled Channel Subject 1

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Equations of Motion for the System of Interest under Time-Dependent Environment F. Sakata, SW. Yan, E-G. Zhao, Y-Z. Zhuo and S-G. Zhou, Prog.Theor.Phys.125,359 (2011) Nakajima-Zwanzig Irrelevant density (t) order-to-chaos Mori Relevant operator B (t) Langevin Eq. There are no theoretical justification to apply for nuclear system time independent temperature, EOS, response function susceptibility/friction coefficient, FD-theory Why they are realized ? Subject 2 We are going to propose a series of papers to make Schroedinger Rep. Heisenberg Rep. Theoretical Development 1: Relevant+Irrelevant+Coupling Interaction Rep. Two requirements should be satisfied !!

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Suppose we already know and by numerical simulation. Let us introduce projection of at time onto relevant subspace To derive FD-theorem (effects of ), let us introduce approximate distribution function under (A): Determining by Coarse-grained Master Equation Theoretical Development 2 (A) During time interval t (macroscopically short, but microscopically long), coupling effects from the relevant dof onto the irrelevant system are negligible (B) relevant motion is described by single (mean) trajectory (like Langevin), irrelevant motion by distribution function (like molecular motion for Brownian particle) Relation to FD-theorem should be clarified !! Coarse-graining dimension Expand with respect to dissipation force and random force are given perturbatively

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Conclusion From Nuclear Physics, Chemical Reaction to Biological Dynamics A. Bohr Transition state (r tr )= (r gr ) Statistical assumption FEBS Lett. 580, 3422 (2006) Folding of Protein Primary, secondary, tertiary and quaternary structure T. Komatsuzaki et al. PNAS98,7666(2001) Super Computer Top3, June 2011 Scientific Discovery through Advanced Computing (K) (Kobe, RIKEN AICS) 1A (Tianhe-1A)(Tianjin, NSCC) Jaguar(Tennessee, ORNL) Dynamics of Emergence Dynamics of Chemical Reaction Fusion Dynamics

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