Europhys. Lett., 61 (2) , pp. 207-213 (2003)
Microscopic theory for the glass transition in a system without static correlationsR. Schilling1 and G. Szamel1, 2
1 Institut für Physik, Johannes Gutenberg-Universität Mainz D-55099 Mainz, Staudinger Weg 7, Germany
2 Department of Chemistry, Colorado State University Ft. Collins, CO 80523, USA
(Received 25 July 2002; accepted in final form 25 October 2002)
We study the orientational dynamics of infinitely thin hard rods of length L, with the centers-of-mass fixed on a simple cubic lattice with lattice constant a. We approximate the influence of the surrounding rods onto dynamics of a pair of rods by introducing an effective rotational diffusion constant D(l), l=L/a. We get , where is given through an integral of a time-dependent torque-torque correlator of an isolated pair of rods. A glass transition occurs at , if . We present a variational and a numerically exact evaluation of . Close to the diffusion constant decreases as , with . Our approach predicts a glass transition in the absence of any static correlations, in contrast to the present form of mode-coupling theory.
61.20.Lc - Time-dependent properties; relaxation.
61.43.Fs - Glasses.
64.70.Pf - Glass transitions.
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