Manacorda Alessandro, Schehr Grégory, Zamponi Francesco
Laboratoire de Physique de l'Ecole Normale Supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université de Paris, F-75005 Paris, France.
Université Paris-Saclay, CNRS, LPTMS, 91405 Orsay, France.
J Chem Phys. 2020 Apr 30;152(16):164506. doi: 10.1063/5.0007036.
We present a numerical solution of the dynamical mean field theory of infinite-dimensional equilibrium liquids established by Maimbourg et al. [Phys. Rev. Lett. 116, 015902 (2016)]. For soft sphere interactions, we obtain the numerical solution by an iterative algorithm and a straightforward discretization of time. We also discuss the case of hard spheres for which we first derive analytically the dynamical mean field theory as a non-trivial limit of that of soft spheres. We present numerical results for the memory function and the mean square displacement. Our results reproduce and extend kinetic theory in the dilute or short-time limit, while they also describe dynamical arrest toward the glass phase in the dense strongly interacting regime.
我们给出了由迈姆堡等人[《物理评论快报》116, 015902 (2016)]建立的无限维平衡液体动力学平均场理论的数值解。对于软球相互作用，我们通过迭代算法和对时间的直接离散化获得数值解。我们还讨论了硬球的情况，为此我们首先通过解析推导得出动力学平均场理论，将其作为软球动力学平均场理论的一个非平凡极限。我们给出了记忆函数和均方位移的数值结果。我们的结果在稀薄或短时间极限下重现并扩展了动力学理论，同时它们也描述了在密集强相互作用区域向玻璃相的动力学阻滞。
