1. T. Odagaki and T. Ekimoto Department of Physics, Kyushu University Ngai Fest September 16, 2006

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

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

4. Separation of time scales Total MicroscopicRelaxation

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

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

7. Three models for g(T) movie

8. The dynamical structure factor of Model 1 0.01T 0 0.1T 0 1T 0 10T 0 100T 0 1000T 0 k=0.5ωS(k,ω) ω Oscillatory motion Jump motion

9. The dynamical structure factor of Model 2 ωS(k,ω) ω k=0.5 0.01T 0 0.1T 0 0.3T 0 10T 0 1000T 0 Jump motion Oscillatory motion

10. The dynamical structure factor of Model 3 k=0.5 ωS(k,ω) ω 100T 0 10T 0 1T 0 0.3T 0 0.1T 0 0.01T 0 Jump motion Oscillatory motion

11. Characteristic time scales

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

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

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

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

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

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

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

19. Unifying concept Characteristic Temperature Equation

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

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

22. Non-Gaussian parameterSusceptibility return