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arXiv 1910.06352cond-mat.softcond-mat.stat-mech
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无序晶体中的非热涨落

Athermal fluctuations in disordered crystals

Pappu Acharya, Surajit Sengupta, Bulbul Chakraborty, Kabir Ramola

摘要:

在弱无序极限下,分析了无序堵塞晶体中粒子位置和粒子间力的涨落。我们证明,这样的非热系统是从根本上不同于他们的热同行,其特征在于约束力垂直于晶格方向的波动。我们开发了一个无序微扰展开的多分散性的结晶状态,我们用它来推导出精确的结果,线性顺序。我们表明,受约束的波动的结果,作为当地的力平衡条件的后果,其特征在于非高斯分布,我们得到确切的。我们分析预测这样的系统的几个属性,包括标度的平均协调与多分散性和包装分数,我们验证与数值模拟使用软盘与单侧谐波相互作用。

英文摘要:

We analyze the fluctuations in particle positions and inter-particle forces in disordered jammed crystals in the limit of weak disorder. We demonstrate that such athermal systems are fundamentally different from their thermal counterparts, characterized by constrained fluctuations of forces perpendicular to the lattice directions. We develop a disorder perturbation expansion in polydispersity about the crystalline state, which we use to derive exact results to linear order. We show that constrained fluctuations result as a consequence of local force balance conditions, and are characterized by non-Gaussian distributions which we derive exactly. We analytically predict several properties of such systems, including the scaling of the average coordination with polydispersity and packing fraction, which we verify with numerical simulations using soft disks with one-sided harmonic interactions.

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