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arXiv 1402.3834cond-mat.soft
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力的分布对硬球玻璃振动特性的影响

The distribution of forces affects vibrational properties in hard sphere glasses

E. DeGiuli, E. Lerner, C. Brito, M. Wyart

摘要:

我们从理论和数值上研究了硬球玻璃的弹性性质,并给出了其力学稳定性的实空间描述。相反,排斥粒子在零温度下,我们认为,存在的某些对粒子相互作用的一个小的力$f$软化弹性性能。这种软化会影响高压下的弹性指数,从而导致实验可检验的预测。表示$P(f)\sim f^{θ_e}$为这种对的力分布,$ϕ_c$为压力发散时的填充分数,我们预测(i)态密度在尺度$ω^*$处具有低频峰,上升到它作为$D(ω) \sim ω^{2+a}$,并在$ω^*$之上作为$D(ω)\sim ω^{-a}$衰减,其中$a=(1-θ_e)/(3+θ_e)$和$ω$是频率,(ii)剪切模量和均方位移与$\langle δR^2\rangle\sim1/μ\sim (ϕ_c-ϕ)^κ $成反比,其中$κ=2-2/(3+θ_e)$,和(iii)连续弹性在尺度$\ell_c \sim1/\sqrt{δz}\sim (ϕ_c-ϕ)^{-b}$上分解,其中$b=(1+θ_e)/(6+2θ_e)$和$δz=z-2d$,其中$z$是坐标,$d$是空间维度。我们数值测试(i),并提供数据支持,$θ_e\approx 0.41$在我们的双分散系统,独立于系统制备的二维和三维,导致$κ\approx1.41$,$a \approx 0.17$,和$b\approx 0.21$。我们的均方位移的结果是一致的,最近的精确副本计算$d=\infty$,而一些意见不同,合理化本方法。

英文摘要:

We study theoretically and numerically the elastic properties of hard sphere glasses, and provide a real-space description of their mechanical stability. In contrast to repulsive particles at zero-temperature, we argue that the presence of certain pairs of particles interacting with a small force $f$ soften elastic properties. This softening affects the exponents characterizing elasticity at high pressure, leading to experimentally testable predictions. Denoting $P(f)\sim f^{θ_e}$ the force distribution of such pairs and $ϕ_c$ the packing fraction at which pressure diverges, we predict that (i) the density of states has a low-frequency peak at a scale $ω^*$, rising up to it as $D(ω) \sim ω^{2+a}$, and decaying above $ω^*$ as $D(ω)\sim ω^{-a}$ where $a=(1-θ_e)/(3+θ_e)$ and $ω$ is the frequency, (ii) shear modulus and mean-squared displacement are inversely proportional with $\langle δR^2\rangle\sim1/μ\sim (ϕ_c-ϕ)^κ $ where $κ=2-2/(3+θ_e)$, and (iii) continuum elasticity breaks down on a scale $\ell_c \sim1/\sqrt{δz}\sim (ϕ_c-ϕ)^{-b}$ where $b=(1+θ_e)/(6+2θ_e)$ and $δz=z-2d$, where $z$ is the coordination and $d$ the spatial dimension. We numerically test (i) and provide data supporting that $θ_e\approx 0.41$ in our bi-disperse system, independently of system preparation in two and three dimensions, leading to $κ\approx1.41$, $a \approx 0.17$, and $b\approx 0.21$. Our results for the mean-square displacement are consistent with a recent exact replica computation for $d=\infty$, whereas some observations differ, as rationalized by the present approach.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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