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arXiv 0902.1888cond-mat.stat-mechcond-mat.dis-nncond-mat.mtrl-sci
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三维玻璃形成系统的统计力学和动力学

Statistical Mechanics and Dynamics of a 3-Dimensional Glass-Forming System

Edan Lerner, Itamar Procaccia, Jacques Zylberg

摘要:

在三维玻璃形成的经典例子的背景下,我们讨论了如何构建玻璃化转变的统计力学理论。该方法的核心是一个简单的标准,用于验证适当选择的放大准物种,允许建设一个理论与有限数量的“状态”。一旦构建,该理论确定了一个典型的规模$ξ$,随着降低温度迅速增加,并确定$α$ -弛豫时间$τ_α$为$τ_α\sim \exp(μξ/T)$与$μ$一个典型的化学势。该理论可以预测在数值模拟无法达到的温度下的弛豫时间。

英文摘要:

In the context of a classical example of glass-formation in 3-dimensions we exemplify how to construct a statistical mechanical theory of the glass transition. At the heart of the approach is a simple criterion for verifying a proper choice of up-scaled quasi-species that allow the construction of a theory with a finite number of 'states'. Once constructed, the theory identifies a typical scale $ξ$ that increases rapidly with lowering the temperature and which determines the $α$-relaxation time $τ_α$ as $τ_α\sim \exp(μξ/T)$ with $μ$ a typical chemical potential. The theory can predict relaxation times at temperatures that are inaccessible to numerical simulations.

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