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

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

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

Separation of time scales Total MicroscopicRelaxation

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

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

Three models for g(T) movie

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

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

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 T 0 Jump motion Oscillatory motion

Characteristic time scales

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

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

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

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

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

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

Trapping Diffusion Model return Waiting time distribution for jump motion

Unifying concept Characteristic Temperature Equation

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

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

Non-Gaussian parameterSusceptibility return