Microscopic theory for the glass transition in a systemwithout static correlations

Abstract

We study the orientational dynamics of infinitely thin hard rodsof length L, with the centers-of-mass fixed on a simple cubiclattice with lattice constant a. We approximate the influenceof the surrounding rods onto dynamics of a pair of rods byintroducing an effective rotational diffusion constant D(l),l = L/a. We get D(l) ∝ [1 − υ(l)], whereυ(l) is given through an integral of a time-dependenttorque-torque correlator of an isolated pair of rods. A glasstransition occurs at lc, if υ(lc) = 1. Wepresent a variational and a numerically exact evaluation ofυ(l). Close to lc the diffusion constantdecreases as D(l) ∝ (lc − l)γ, with γ = 1.Our approach predicts a glass transition in the absence of anystatic correlations, in contrast to the present form of mode-coupling theory.