标题： Replicated liquid theory in $1+\infty$ dimensions 显示英文标题

标题： Replicated liquid theory in $1+\infty$ dimensions

摘要： 我们开发了一种复制液体理论，用于研究沿某一轴（例如$z$轴）表现出物理量空间变化的结构玻璃。该理论在无限横向维度$d-1 \to \infty$时是精确的。它提供了一个具有空间依赖的玻璃序参数$\Delta_{ab}(z)$的精确自由能泛函。作为该方案的首次应用，我们研究了硬球在有/无限制腔体情况下与动态/静态玻璃转变相关的发散长度。指数与之前对相关平均场模型的研究结果一致。此外，它预测了在腔体内玻璃序参数$\Delta_{ab}(z)$的非平凡空间分布，该分布在接近动态玻璃转变时表现出标度特征。 显示英文摘要

摘要： We develop a replicated liquid theory for structural glasses which exhibit spatial variation of physical quantities along one axis, say $z$-axis. The theory becomes exact with infinite transverse dimension $d-1 \to \infty$. It provides an exact free-energy functional with space-dependent glass order parameter $\Delta_{ab}(z)$. As a first application of the scheme, we study diverging lengths associated with dynamic/static glass transitions of hardspheres with/without confining cavity. The exponents agree with those obtained in previous studies on related mean-field models. Moreover, it predicts a non-trivial spatial profile of the glass order parameter $\Delta_{ab}(z)$ within the cavity which exhibits a scaling feature approaching the dynamical glass transition.