1. Free Energy Landscape -Evolution of the TDM- Takashi Odagaki Kyushu University IV WNEP Round Table Discussion September 22, 2006 Trapping diffusion Model

2. What do we have to understand? Thermodynamics Thermodynamics What is the transition? What is the transition? Cooling rate dependence? Cooling rate dependence? T g ? T K ? T g ? T K ? Slow process Fast process Dynamics Dynamics Slow dynamics? T 0 ? Slow dynamics? T 0 ? Fast dynamics? Fast dynamics? T g ? T x ? T g ? T x ?

3. How do we proceed? Phenomenological Understanding of Experiments of Experiments Fundamental Theory New Paradigm

4. 2 nd order Phase TransitionGlass transition Configuration Free energy Degree of quenching (t obs )= Annealedquenched disorderedordered doq At Slow & fast relaxations

5. Trapping diffusion model Single particle description of the FEL picture Waiting time distribution Findings Gaussian – non-Gaussian Transition at Characteristic Temperature Equation

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

7. 20 basins:Einstein oscillators slow fast Specific heat Probability of being in basin a at t Energy of basin a a annealed quenched Findings Annealed to quenched transition Cooling rate dependence Characteristic behaviors of ac specific heatCharacteristic behaviors of ac specific heat

8. Conclusion The FEL picture is the only frame work that provides unified understanding of the glass transition. The FEL picture is the only frame work that provides unified understanding of the glass transition. The FEL can be constructed by the The FEL can be constructed by the The FEL can be constructed by the The FEL can be constructed by the density functional approach. density functional approach. Remark

9. The 1 st order ac specific heat  Debye Return

10. The 2 nd order ac specific heat Real part Imaginary part Return

11. Free energy landscape For practical calculation for where Separation of microscopic and structural-relaxation time scales : Direct correlation function Ramakrishnan-Yussouff free energy functional for hard spheres

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

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