Clarification and Questions on

“Growing Length and Time Scales in Glass-forming Liquids”

Ryoichi YamamotoKyoto University

Summary of Dasgupta’s talk

Introduced a “temporal quantity Q(t0)” which is sensitive to particle motions associated with a microscopic length scale “a” and a lag time ”t”.

Introduced a “temporal quantity Q(t0)” which is sensitive to particle motions associated with a microscopic length scale “a” and a lag time ”t”.

Then, set “a=0.3” and “=”. Then, set “a=0.3” and “=”.

Summary of Dasgupta’s talk

average part (later)average part (later)

fluctuating partfluctuating part

Summary of Dasgupta’s talk

consistent

OK, FSS seems to work for the “fluctuating” part.

OK, FSS seems to work for the “fluctuating” part.

Examined FSS for χ4 and B. Examined FSS for χ4 and B.

Summary of Dasgupta’s talk

FSS doesn’t work for the average relaxation time...

FSS doesn’t work for the average relaxation time...

Next, examined FSS for the structural relaxation time.Next, examined FSS for the structural relaxation time.

Summary of Dasgupta’s talk

Q1: FSS seems to work well for the “fluctuation part” but fails for the “average part”. Does this statement make sense? Q1: FSS seems to work well for the “fluctuation part” but fails for the “average part”. Does this statement make sense?

Summary so far...Summary so far...

Summary of Dasgupta’s talk

Finaly, try FSS for Configurational Entropy.Finaly, try FSS for Configurational Entropy. Very interesting results, but still confusing...

FSS seems to work for Sc, but the fitted values of do not mach with those from χ4 or B at all.

The relaxation time fits very well with AG fitting.

Very interesting results, but still confusing...

FSS seems to work for Sc, but the fitted values of do not mach with those from χ4 or B at all.

The relaxation time fits very well with AG fitting.

Q2: What does this result suggest ? Decoupling of glowing time scale and glowing length scale with decreasing system size?? Q2: What does this result suggest ? Decoupling of glowing time scale and glowing length scale with decreasing system size??

Critical Slowing-down (’60-early ’70)fluctuations in “order parameter “fluctuations in “order parameter “

This is so-called critical slowing-down. Glowing length directly leads to the slowing-down!!This is so-called critical slowing-down. Glowing length directly leads to the slowing-down!!

need MCTneed MCT

time-space correlation (2-point)time-space correlation (2-point)

Langevin Eq. Langevin Eq.

Glass Transition as CP (late ’90-)fluctuations in “local dynamics”fluctuations in “local dynamics”

time-space correlation (4-point)time-space correlation (4-point)

4-point relaxation time(migration time of DH)

2-point relaxation time(usual relaxation time)

average relaxation average relaxation

RY&Onuki (’97, ‘98), Glotzer (‘99), Berthier (‘04), Weeks (?), IMCT (‘06),...

any physics??any physics??

coupling??coupling??

General Questions

1. What is the true identity of the DH and glowing length scale ξ? a. Any correspondence with static properties?b. Mosaic phase? Hidden order parameters? CRR?

How can we identify them???

2. What is the main role of the glowing length scale ξ?a. We have no proper theory for bridging between glowing

length scale (ξ) and glowing time scales (4,k, qm).

b. GT vs. CP -> more differences than similarities.c. Does ξ contribute to slowdown the system, or accelerate it?

(Remember Weeks’ talk.)d. Is ξ nothing more than a by-product of slowing-down?

Thank you for your attention !

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