Biroli Giulio, Bouchaud Jean-Philippe, Miyazaki Kunimasa, Reichman David R
Service de Physique Théorique, Orme des Merisiers-CEA Saclay, 91191 Gif sur Yvette Cedex, France.
Phys Rev Lett. 2006 Nov 10;97(19):195701. doi: 10.1103/PhysRevLett.97.195701. Epub 2006 Nov 6.
We extend mode-coupling theory (MCT) to inhomogeneous situations, relevant for supercooled liquid in an external field. We compute the response of the dynamical structure factor to a static inhomogeneous external potential and provide the first direct evidence that the standard formulation of MCT is associated with a diverging length scale. We find that the so-called cages are, in fact, extended objects. Although close to the transition the dynamic length grows as |T-T(c)|(-1/4) in both the beta and alpha regimes, our results suggest that the fractal dimension of correlated clusters is larger in the alpha regime. We derive inhomogeneous MCT equations valid to second order in gradients.
我们将模式耦合理论（MCT）扩展到非均匀情形，这与处于外场中的过冷液体相关。我们计算了动态结构因子对外加静态非均匀势的响应，并首次直接证明了MCT的标准公式与一个发散的长度尺度相关。我们发现，所谓的笼实际上是扩展对象。尽管在β和α区域接近转变时动态长度都以|T - T(c)|^(-1/4)的形式增长，但我们的结果表明，相关团簇的分形维数在α区域更大。我们推导了在梯度上二阶有效的非均匀MCT方程。
