椭球玻璃中Gardner转变的研究

近来平均场理论副本对称破缺(RSB)被成功应用到结构玻璃上，并预测在深度过冷液体发生普通玻璃到Gardner相玻璃的转变，Gardner转变是类二级相变， Gardner相玻璃具有层级结构的自由能景观。RSB理论没有包含低维玻璃的情况。分子模拟显示，从准一维到三维具有硬球极限的玻璃体系依然存在Gardner相玻璃，但是与理论预言的不同，Gardner转变只是一个交叉点(crossover)。在软球体系(比如Lennard-Jones)，尽管发现了被认为与Gardner物理相关的局域化缺陷，然而却没有探测到Gardner相玻璃。.硬椭球与圆球相比不同的是hypostaticity，即相互接触的配位数小于自由度的数目，违反了Maxwell力学稳定准则，导致了力和间隔分布不再具有幂律分布，此幂律行为在圆球体系被认为是临界稳定的条件。我们将运用分子模拟研究椭球的特殊性如何影响Gardner物理。

Up on fast cooling or compression, a liquid can undergoes glass transition with sluggish dynamics, glass is solid but its structure is similar to liquid. Understanding the nature of glass transition and glassy state is one of the most important issues. Despite the existence of many theories about the glassy state, most of them are phenomenological and tailored for specific problems. Recently, a mean field theory, i.e. replica symmetry breaking (RSB), which originates from the mean- field theory of spin glasses. has been successfully applied to structural glass: it predicts that there is a Gardner transition in the deeply supercooled liquid, at least in high dimensions (d≥6). The Gardner transition is second order-like, with diverging correlation length, susceptibility, etc., The resulting Gardner phase has hierarchical landscape of free energy and is marginal stable. Recent molecular simulation results show that even in physically accessible dimensions (i.e., from quasi-one dimension to three dimension), the Gardner phase still exists in the hard-sphere limit: the difference is that the Gardner transition in these systems just shows up as a crossover, i.e. no diverging correlation length and susceptibility, etc.. However, in soft-particle systems (e.g., Lennard Jones), the Gardner phase is absent, although localized defects are detected, which are considered to be related to the Gardner physics. At this stage, an explanation for this behavior is lacking. So the question remains to what extent, the Gardner physics scenario still holds in real systems..Amorphous packings of nonspherical particles such as ellipsoids are known to be hypostatic: The number of mechanical contacts between particles is smaller than the number of degrees of freedom, thus violating Maxwell’s mechanical stability criterion. Recent theory work reveals that hypostaticity can result in the breakdown of the power-law behavior of the force and gap distributions near the jamming point. This behavior contrasts with isostatic jamming of spherical particles. In fact, power-law behavior of the force and the gap is considered to be an essential condition for marginal stability near jamming point. Our project will investigate how the absence of two this power-law behavior will affect the Gardner physics.