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arXiv 1608.05919cond-mat.soft
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热致非晶态固体中的粒子间相互作用

Emergent Inter-particle Interactions in Thermal Amorphous Solids

Edan Lerner, Yoav G. Pollack, Itamar Procaccia, Birte Riechers

摘要:

在有限温度下的无定形介质,无论是液体、胶体还是玻璃,都是由相互作用的粒子组成的,这些粒子由于热能而混乱地运动,不断地相互碰撞和散射。当这些系统中的平均构型仅在长时间内松弛时,可以引入{ \em有效相互作用},其使{ \em平均位置}保持在机械平衡中。我们引入了一个新的框架来确定这些有效的力的法律,定义了一个有效的海森,可以用来讨论稳定性和非晶系统的状态密度。我们用一种由硬球组成的热玻璃来代替这种方法;这些球在不接触时感觉到零力,而在接触时感觉到无穷大的力。本方法重新捕获了有效的相互作用,对于在温度下足够致密的球体,$T$取决于球体之间的间隙$h$,如$T/h$ [C. Brito和M.怀亚特,欧罗巴。Lett. 76 149(2006)]。在较低密度或具有较长微观相互作用的系统中(例如Lennard-Jones),涌现力定律将包括三元,四元和通常更高阶的多体项,即使微观相互作用是严格的二元。

英文摘要:

Amorphous media at finite temperatures, be them liquids, colloids or glasses, are made of interacting particles that move chaotically due to thermal energy, colliding and scattering continuously off each other. When the average configuration in these systems relaxes only at long times, one can introduce {\em effective interactions} that keep the {\em mean positions} in mechanical equilibrium. We introduce a new framework to determine these effective force-laws that define an effective Hessian that can be employed to discuss stability properties and density of states of the amorphous system. We exemplify the approach with a thermal glass of hard spheres; these feel zero forces when not in contact and infinite forces when they touch. The present approach recaptures the effective interactions which for sufficiently dense spheres at temperature $T$ depends on the gap $h$ between spheres as $T/h$ [C. Brito and M. Wyart, Europhys. Lett. 76 149 (2006)]. In systems at lower densities or with longer microscopic interaction (say like Lennard-Jones), the emergent force laws will include ternary, quaternary and generally higher order many-body terms, even if the microscopic interactions are strictly binary.

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