液晶Lebwohl-Lasher模型中的时间关联函数
Time correlation functions in the Lebwohl-Lasher model of liquid crystals
摘要：
用理论和分子动力学模拟研究了液晶液晶Lebwohl-Lasher模型中的时间关联函数。特别地，在长波长极限下计算了角动量和指向矢涨落的自相关函数。流体动力学电流的本构关系推导出使用一个标准的程序的基础上的非负熵产生。然后将连续性方程线性化并求解以计算关联函数。我们发现横向角动量涨落与指向矢涨落耦合，并且都是传播的。波动的传播性质抑制了单粒子自相关函数中预期的流体动力学长时间尾。然而，各向同性相中的波动是扩散性的，导致$d$空间维度中的$t^{-d/2}$长时间拖尾。用时间-关联函数测量的Frank弹性常数与以前报道的结果吻合得很好。
英文摘要：
Time correlation functions in the Lebwohl-Lasher model of nematic liquid crystals are studied using theory and molecular dynamics simulations. In particular, the autocorrelation functions of angular momentum and nematic director fluctuations are calculated in the long-wavelength limit. The constitutive relations for the hydrodynamic currents are derived using a standard procedure based on non-negativity of the entropy production. The continuity equations are then linearized and solved to calculate the correlation functions. We find that the transverse angular momentum fluctuations are coupled to the director fluctuations, and are both propagative. The propagative nature of the fluctuations suppress the anticipated hydrodynamic long-time tails in the single-particle autocorrelation functions. The fluctuations in the isotropic phase are however diffusive, leading to $t^{-d/2}$ long-time tails in $d$ spatial dimensions. The Frank elastic constant measured using the time-correlation functions are in good agreement with previously reported results.
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