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arXiv 1507.03421cond-mat.stat-mechcond-mat.dis-nncond-mat.soft
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液体动力学的高维极限解

Solution of the dynamics of liquids in the large-dimensional limit

Thibaud Maimbourg, Jorge Kurchan, Francesco Zamponi

备注：
4 pages + Appendix with 25 pages and 5 figures
发表信息：
Phys. Rev. Lett. 116, 015902 (2016)
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摘要：

我们得到了球形粒子液体的时间关联函数的解析表达式，精确到高维极限$d$。推导过程很长，但很简单：一个动态维里展开，只有前两项生存，其次是广义球坐标的动态变量的变化，导致鞍点评估大$d$的积分。因此，问题被映射到一维扩散的扰动谐波势与色噪声。在高密度下，发现了一个遍历性破坏的玻璃化转变，在这个区域，我们的结果与热力学相一致，与一般的随机一级转变的情况相一致。的玻璃化转变密度是高于最好的已知的下限硬球填料在大$d$。由于我们的计算是初等的，即使不是严格的，也是初等的，因此，在大维度中，球填充的界的改进就在眼前。

英文摘要：

We obtain analytic expressions for the time correlation functions of a liquid of spherical particles, exact in the limit of high dimensions $d$. The derivation is long but straightforward: a dynamic virial expansion for which only the first two terms survive, followed by a change to generalized spherical coordinates in the dynamic variables leading to saddle-point evaluation of integrals for large $d$. The problem is thus mapped onto a one-dimensional diffusion in a perturbed harmonic potential with colored noise. At high density, an ergodicity-breaking glass transition is found. In this regime, our results agree with thermodynamics, consistently with the general Random First Order Transition scenario. The glass transition density is higher than the best known lower bound for hard sphere packings in large $d$. Because our calculation is, if not rigorous, elementary, an improvement in the bound for sphere packings in large dimensions is at hand.

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