论文标题
无定形媒体的Hessian元素分布中的奇异性
Singularities in Hessian element distributions of amorphous media
论文作者
论文摘要
我们表明，与无定形材料相关的Hessian矩阵中元素的分布表现出奇异性$ p（h）\ sim {\ lvert h \ rvert}^γ$，带有指数$γ<0 $，as $ \ lvert h \ lvert h \ rvert \ to 0 $。我们利用了无定形结构中潜在疾病的旋转不变性，以通过径向对称势相互作用来推导这些指数。我们表明，$γ$仅取决于截止距离构成粒子之间相互作用潜力的平滑度$ n $的程度，而与两个和三维相互作用的细节无关。我们通过对结构玻璃形成器模型的数值模拟来验证我们的预测。最后，我们表明，这种奇异性通过Hessian矩阵的最低特征值的分布影响了无定形固体的稳定性。
We show that the distribution of elements $H$ in the Hessian matrices associated with amorphous materials exhibit singularities $P(H) \sim {\lvert H \rvert}^γ$ with an exponent $γ< 0$, as $\lvert H \rvert \to 0$. We exploit the rotational invariance of the underlying disorder in amorphous structures to derive these exponents exactly for systems interacting via radially symmetric potentials. We show that $γ$ depends only on the degree of smoothness $n$ of the potential of interaction between the constituent particles at the cut-off distance, independent of the details of interaction in both two and three dimensions. We verify our predictions with numerical simulations of models of structural glass formers. Finally, we show that such singularities affect the stability of amorphous solids, through the distributions of the minimum eigenvalue of the Hessian matrix.
