Depken Martin, Stinchcombe Robin
Department of Physics, Theoretical Physics University of Oxford, 1 Keble Road, Oxford, OX1 3NP, United Kingdom.
Phys Rev E Stat Nonlin Soft Matter Phys. 2005 Jun;71(6 Pt 2):065102. doi: 10.1103/PhysRevE.71.065102. Epub 2005 Jun 13.
We analytically study a one-dimensional compaction model in the glassy regime. Both correlation and response functions are calculated exactly in the evolving dense and low tapping strength limit, where the density relaxes in a 1/ln t fashion. The response and correlation functions turn out to be connected through a nonequilibrium generalization of the fluctuation-dissipation theorem. The initial response in the average density to an increase in the tapping strength is shown to be negative, while on longer time scales it is shown to be positive. On short time scales the fluctuation-dissipation theorem governs the relation between correlation and response, and we show that such a relationship also exists for the slow degrees of freedom, albeit with a different temperature. The model is further studied within the statistical theory proposed by Edwards and co-workers, and the Edwards entropy is calculated in the large system limit. The fluctuations described by this approach turn out to match the fluctuations as calculated through the dynamical consideration. We thus have an instance where these ideas can be confirmed analytically in a non-mean-field model.
我们对玻璃态区域中的一维压实模型进行了分析研究。在演化的致密且低敲击强度极限下，精确计算了关联函数和响应函数，在此极限下密度以1/ln t的方式弛豫。响应函数和关联函数通过涨落耗散定理的非平衡推广相互联系。平均密度对敲击强度增加的初始响应被证明是负的，而在较长时间尺度上则是正的。在短时间尺度上，涨落耗散定理支配着关联和响应之间的关系，并且我们表明，对于慢自由度也存在这样的关系，尽管温度不同。在爱德华兹及其同事提出的统计理论框架内对该模型进行了进一步研究，并在大系统极限下计算了爱德华兹熵。结果表明，这种方法所描述的涨落与通过动力学考虑计算出的涨落相匹配。因此，我们有一个实例，其中这些观点可以在非平均场模型中通过解析得到证实。
