Regensburg 2010 – wissenschaftliches Programm

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CPP: Fachverband Chemische Physik und Polymerphysik

CPP 39: Glasses and Glass Transition II (jointly with DY and DF)

CPP 39.5: Vortrag

Donnerstag, 25. März 2010, 10:45–11:00, H38

Glass transition in high dimensions — •Bernhard Schmid and Rolf Schilling — Institut für Physik, Johannes Gutenberg-Universität Mainz, Staudinger Weg 7, D-55099 Mainz, Germany

We have studied the glass transition of hard spheres with diameter σ for dimensions d→ ∞ in the framework of mode-coupling theory (MCT). Assuming that the direct correlation function equals the Mayer function in the limit of high dimensions, we have solved numerically the MCT equations [1] up to d=800. The numerical results for the critical collective and self nonergodicity parameters f_c( k;d) and f_c^{( s)} ( k;d) exhibit no Gaussian k-dependence even for d=800. Instead they can be represented by a master function, which vanishes for kσ >k₀d^3/2 with k₀≅ 0.15. Inspired by these results, we were able to prove analytically that f_c( k;d) converges to f_c^{( s)} ( k;d) for kσ =O( d) and d→ ∞ and that the critical packing fraction is given by ϕ _c( d) ∼ d²2^−d. The non-Gaussian character of f_c( k;d) and f_c^{( s)} ( k;d) implies that the hard sphere glass at ϕ _c( d) is not a harmonic solid, even in the limit of high dimensions.

[1] M. Bayer, J.M. Brader, F. Ebert, M. Fuchs, E. Lange, G. Maret, R. Schilling, M. Sperl and J.P. Wittmer, Phys. Rev. E 76, 011508 (2007)