Toward a Dynamics of Emergence - On the long way I walked along with Professor Zhuo -

Fumihiko SakataProfessor Emeritus, Ibaraki University

Member of the board of directors, Gushinkai Foundation

Talk presented atChina Institute of Atomic Energy, Oct. 19, 2011

慶祝　傘寿　卓益忠教授

Introduction

http://blogs.openaccesscentral.com/ccblog/

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 2001-3) 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

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 Reactionhttps://www.cps-jp.org/~21coeps/pub/POSTER/PDF/sg03-Cross-Talk.pdf

nuclear fission process

Poincare section mapof standard map

Transition state theoryHenry Eyring, JCP3(1935)107

Micro-level Dynamics

Described bySchrödinger Eq. for

Constituent Particles

Microscopic Numerical Simulation Ab-initio (GF Monte Carlo) , ConfigulationInteraction, density functional Theory

Reduction Principle of dof Projection Operator Method Coarse-Graining ProcedureMemory EffectsScale Separation

Dynamics of Protein Folding and conformationJ. Am. Chem. Soc., 2010, 132 (38), 13129

http://pubs.acs.org/doi/abs/10.1021/ja105206w

Macro-level Dynamicsdescribed 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

Microscopic Equation

High-PerformanceComputer

Experiment

Black Box

Treasure Box

Emergence of Macro-Dynamics out of Micro-Dynamics

Dynamicsof

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

Equations of Motion for the System of Interest under Time-Dependent EnvironmentF. 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 functionsusceptibility/friction coefficient, FD-theory

Why they are realized ?

Subject 2

We are going to propose a series of papers to make

Schroedinger Rep.

HeisenbergRep.

Theoretical Development 1:

Relevant+Irrelevant+Coupling

InteractionRep.

Two requirements should be satisfied !!

Suppose we already know and by numerical simulation. Let us introduce projection of at time ontorelevant 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 todissipation force and randomforce are given perturbatively

Conclusion

From Nuclear Physics, Chemical Reaction to Biological Dynamics

A. Bohr Transition state

(rtr)=(rgr)

Statisticalassumption

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

京 (K) (Kobe, RIKEN AICS)天河 1A 号 (Tianhe-1A)(Tianjin, NSCC)Jaguar(Tennessee, ORNL)

Dynamicsof

Emergence

Dynamics of Chemical Reaction

Fusion Dynamics