Derivation of Coarse-grained Macroscopic Equation - Instruction for Application -

1. Derivation of Coarse-grained Macroscopic Equation - Instruction for Application - Presentation givenat Institute of Theoretical Physics, October. 11, 2011 Fumihiko Sakata Professor Emeritus, Ibaraki University Member of the board of directors, Gushinkai Foundation

2. Introduction Searching for Dynamics of Emergence (Evolution of Matter) Emergence “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, … Nucleus Finite, self-sustained, Strongly interacting, nonlinear complex system • Organ System •  Animal

3. Science in the Era of High Performance Computer Covering Physics, Climate, Groundwater, Fusion Energy, Life Sciences Materials & Chemistry DOE-Project Theoretical Nuclear Physics Ab-initio Calculation of Nuclear Structure and Reaction Green’s function Monte Carlo (GFMC) No-core shell model (NCSM) Nuclear Energy Density Functional Theory (EDFT) What do we learn from numerical calculation Black Box ? High-Performance Computer Experiment Microscopic Equation Dynamics of Emergence 京(K) (Kobe, RIKEN AICS) 天河1A号(Tianhe-1A)(Tianjin, NSCC) Jaguar(Tennessee, ORNL)

4. How to understand Emergence Dynamics in Nuclei What actually happens in HI-DIC, nuclear fusion and fission ・ microscopic origin of dissipation and fluctuation described in macroscopic variables ・ role of one- and two-body dissipation (mean-field and correlation/macro and micro) ・ role of adiabatic- and diabatic-mean field ・ role of macro (mean field) variables (window, wall, neck, asymmetry, friction,…) ・ role of various reaction process (one, two and many nucleon transfer, successive transfer,…) http://euroball.lnl.infn.it/ECTbigs/talks/Bob_Chapman.pdf There are no general quantum many-body reaction theory !! superposition of nn-scattering two body scattering V.I.Zagrebaev, PRC64,034606(2001)

5. Microscopic Equation Numerical Simulation describing - Change of Nuclear Structure as well as Reaction Process - Time-Dependent Variational Principle There are no general quantum many-body reaction theory !! (Later discussion) Simulation is needed like gravitational n-body problem TDVP associates to a Hamiltonian quantum system a set of trajectories running on a classical phase space Classical image (e.g.; Wigner transformation) Canonical Eqs. of Motion

6. Time-Dependent HartreeFock (mean field: ph-amplitudes) Fermion Molecular Dynamics (wave packet: central values of coordinate & momentum) spatial⊗spin&isospin Gaussian wave packet Trial state for N nucleon system Basic equation of FMD How to describe different reaction channel + + various sequential Reactions xj(A) Intrinsic coordinate of system A Transfer Reaction A(a, b)B : B=A+n, a=n+b • Elastic, Inelastic A(a, a’)A’

7. Elastic and inelastic Collision Single-Nucleon Transfer Reaction General Hamiltonian in parameter space Hamiltonian in elastic and inelastic collision Center of mass + Intrinsic + Relative + Coupling

8. How to understand Numerical Simulation Liouville Equation for Distribution Function r(t) Time Development of Dynamical Variable B(t) There holds a relation Multi-Channel Reaction is determined by numerical simulation Relevant dof Irrelevant dof

9. Modified Time-Dependent Projection Operator Method Two basic assumptions relavant motion is described by single (mean) trajectory (like Langevin), irrelevant motion by distribution function (like Brownian motion) During Dt (macroscopically short, microscopically long), coupling effects from the relevant dof onto the irrelevant system are negligible is well described by ? Irrelevant Relevant Formal solution Initial condition mean-effect fluctuation effects Project onto relevant space

10. Taking account of order-to-chaos transition in irrelevant system Coarse-Grained Macroscopic Hamiltonian Integration over instead of Expand in terms of origin of random force as well as dissipation force for relevant motion is evaluated term by term appearing in perturbative treatment of . Define small time interval (microscopically long) next step ; initial condition to get = c.f. PTP125(2011)359 Coarse-grained equation Coarse-grained dimension e

11. Some Remarks TDHF basic dynamics and anti-symmetrization are included FMD quantum mechanical Simplifications are needed same width of wave packets anti-symmetrization: let us start with a few high momentum nucleons are transferred (N+M), (N+1,M-1)+/-(N-1,M+1),…are important wall of initial nuclei are important V.I.Zagrebaev, PRC64,034606(2001)