Discussion of Itamar’s talk, August 2008

1. Discussion of Itamar’s talk, August 2008 T. Witten, University of Chicago

2. Responding to Itamar’s picture of glassy state Itamar’s talk raises basic issues, challenges conventional wisdom What do we think of these challenges? Summarize the distinctive aspects of Itamar’s model Points we probably agree with Points we may not agree with

3. Basic strategy: identified local defects Main assertion: simple motions of readily identified local structure account for the macroscopic relaxation This strategy is accepted and successful in dislocation plasticity in metal crystals topological defect annealing in liquid crystals... Itamar’s defects: Voronoi cells labeled by their number of edges and content 5, 6, 7 sides, big or small particle inside Every real configuration (that counts) is associated with a cell assignment Itamar’s dynamics: T_1 flips, as in foam cells Every continuous motion of the particles corresponds to a specific sequence of flips ASSERTION: simple equilibrium kinetics of these cells by these flips  glassy relaxation

4. Itamar’s Minimal model of how cells evolve Obtain mean energy and volume of each cell type from a real simulation Evolve cell population using T_1 moves using equilibrium kinetics Tractable by conventional stat. mech. Conclude: certain “liquidlike” (7s, 5L) disappear at low temperature (as observed) Density quantitatively predicted Connection to relaxation observe that fluidity requires these “liquidlike” cells 7s + 5L 0 Dynamic relaxation: annihilation reaction Activation energy to annihilate is argued proportional to their separation Thus low density  super-Arrhenius slow relaxation times as observed in the simulation.

5. Meaning of Itamar’s strategy: what’s at stake? Do locally determined objects and motions explain glassy relaxation as they explain relaxation of other systems? Why not? It seems to work.

6. Things we probably agree with Itamar’s choice of defects and moves is plausible (though other choices seem possible) Ergodicity: Itamar argues that after sufficient time even a glass of finite size is ergodic. Not in dispute (argument places no limit on the time required). Vogel-Fulcher temperature is not a real freezing of all relaxation Entropy does not vanish at a nonzero temperature. Itamar’s minimal model if executed numerically could well give long, relaxation like the microscopic simulation.

7. Things we may not agree with That Itamar’s choice of defects has microscopic significance Cf. dislocation lines T_1 flips in a foam .... Other choices are also plausible: eg. cells with extra large or small volume. Such cells would also go away at low temperature. Do the cells have a robust identity? Are the variations in energy within one type smaller than the difference between types? Are T1 flips the rate-limiting local steps as in a foam? Activation barrier? Many attempts before successful T1? Do they explain spatial heterogeneity? (This feature offers hope to overcome the ambiguity of global relaxation measurements) Do liquidlike cells proliferate in regions observed to be mobile?

9.           