T. Odagaki and T. Ekimoto Department of Physics, Kyushu University

1. Ngai Fest September 16, 2006 Fast and Slow Dynamics in the Free Energy Landscape T. Odagaki and T. Ekimoto Department of Physics, Kyushu University

2. High T High T Low T Free energy Low T Free energy Phase transition Order parameter Configuration Phase Transition Glass transition : Diverging mean waiting time Free Energy Landscape

3. Dynamics Single particle:Gaussian to non-Gaussian transition Slow and fast relaxations Thermodynamics Specific heat: Annealed to quenched transition Cooling-rate dependence Construction of free energy landscape Dynamics Thermodynamics Phenomenology Slow and fast relaxations Fundamental Theory

4. Separation of time scales Total Microscopic Relaxation

5. Separation of time scales for where For practical calculation : Random force Free energy landscape Dynamics on the FEL [Ansatz]

6. A toy model for the dynamics on the FEL Dynamics Scaled equation random force and

7. Three models for g(T) movie

8. The dynamical structure factor of Model 1 ωS(k,ω) k=0.5 Jump motion 1000T0 100T0 10T0 1T0 0.1T0 Oscillatory motion 0.01T0 ω

9. The dynamical structure factor of Model 2 ωS(k,ω) k=0.5 Jump motion 1000T0 10T0 0.3T0 0.1T0 0.01T0 Oscillatory motion ω

10. The dynamical structure factor of Model 3 ωS(k,ω) k=0.5 Jump motion 100T0 10T0 1T0 0.3T0 0.1T0 Oscillatory motion 0.01T0 ω

11. Characteristic time scales

12. Unified Theory for Glass Transition Single particle:Gaussian to non-Gaussian transition Slow and fast relaxations Specific heat: Annealed to quenched transition Cooling-rate dependence Construction of free energy landscape Dynamics Thermodynamics Phenomenology Dynamics Thermodynamics Fundamental Theory

13. : Direct correlation function Ramakrishnan-Yussouff free energy functional Free energy landscape as a function of

14. No of atoms in the core ：32 Ｓｔｒｉｎｇ　ｍｏｔｉｏｎ and CRR

15. Simultaneously and cooperatively rearranging regions SRR: Difference between two adjacent basins CRR: Atoms involved in the transition state return

16. Energy of basin a Probability of being in basin a at t a ：Quenched ：Annealed Phenomenological understanding : Heat capacity T. Tao &T.O(PRE 2002),T.O et al (JCP 2002),T. Tao et al (JCP2005)

17. slow fast T. Tao, T. O and A. Yoshimori: JCP 122, 044505 (2005) • 20 basins:Einstein oscillators Annealed-to-quenched transition and cooling rate dependence return

18. Waiting time distribution for jump motion Trapping Diffusion Model return

19. Characteristic Temperature Equation Unifying concept

20. Characteristic Temperature Equation V B Kokshenev & P D Borges, JCP 122, 114510 (2005) return

21. :Size of CRR by Adam and Gibbs CRR Prob. of activation free energy Waiting time distribution SRR Waiting time distribution for slow relaxation return

22. Non-Gaussian parameter Susceptibility return