Yoshino Hajime, Zamponi Francesco
Department of Earth and Space Science, Faculty of Science, Osaka University, Toyonaka 560-0043, Japan and Cybermedia Center, Osaka University, Toyonaka, Osaka 560-0043, Japan.
LPT, École Normale Supérieure, UMR 8549 CNRS, 24 Rue Lhomond, 75005 Paris, France.
Phys Rev E Stat Nonlin Soft Matter Phys. 2014 Aug;90(2):022302. doi: 10.1103/PhysRevE.90.022302. Epub 2014 Aug 20.
We compute the shear modulus of amorphous hard and soft spheres, using the exact solution in infinite spatial dimensions that has been developed recently. We characterize the behavior of this observable in the whole phase diagram, and in particular around the glass and jamming transitions. Our results are consistent with other theoretical approaches, which are unified within this general picture, and they are also consistent with numerical and experimental results. Furthermore, we discuss some properties of the out-of-equilibrium dynamics after a deep quench close to the jamming transition, and we show that a combined measure of the shear modulus and of the mean square displacement allows one to probe experimentally the complex structure of phase space predicted by the full replica-symmetry-breaking solution.
我们利用最近发展出的无限空间维度中的精确解，计算了非晶态硬球和软球的剪切模量。我们刻画了这个可观测量在整个相图中的行为，特别是在玻璃化转变和堵塞转变附近的行为。我们的结果与其他理论方法一致，这些方法在这个总体框架内是统一的，并且也与数值和实验结果一致。此外，我们讨论了在接近堵塞转变处深度淬火后的非平衡动力学的一些性质，并且我们表明，剪切模量和均方位移的联合测量允许人们通过实验探测由完全复制对称破缺解预测的相空间的复杂结构。
