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 D ( l ) ∝ [1 − υ( l )], where υ( l ) is given through an integral of a time-dependent torque-torque correlator of an isolated pair of rods. A glass transition occurs at l c , if υ( l c ) = 1. We present a variational and a numerically exact evaluation of υ( l ). Close to l c the diffusion constant decreases as D ( l ) ∝ ( l c − l ) γ , with γ = 1. Our approach predicts a glass transition in the absence of any static correlations, in contrast to the present form of mode-coupling theory.
No takes yet. Share an insight, caveat, or question.
A 2003 study studied this question.