Maier-Saupe势再取向的概率分布函数
Probability distribution function for reorientations in Maier-Saupe potential
摘要：
非惯性转动扩散方程概率分布函数的精确解析解，Smoluchowski单轴平均力矩势的一个推广，在对称的Maier-Saupe单轴平均力矩势中，通过汇合Heun函数得到了Smoluchowski单轴平均力矩势的一个推广.考虑了普通Maier-Saupe势和变势垒宽度的双阱势。因此，本文通过将Smoluchowski方程简化为汇合Heun方程，大大扩展了适用于处理的势的范围。该解对任何势垒高度都是一致有效的。我们用它来计算平均首次通过时间。同时计算了普通Maier-Saupe势情况下弛豫衰变模的高本征值。所得结果与Coffey、Kalmykov、Déjardin及其合著者在整个势垒高度范围内的方法完全一致。
英文摘要：
Exact analytic solution for the probability distribution function of the non-inertial rotational diffusion equation, i.e., of the Smoluchowski one, in a symmetric Maier-Saupe uniaxial potential of mean torque is obtained via the confluent Heun's function. Both the ordinary Maier-Saupe potential and the double-well one with variable barrier width are considered. Thus, the present article substantially extends the scope of the potentials amenable to the treatment by reducing Smoluchowski equation to the confluent Heun's one. The solution is uniformly valid for any barrier height. We use it for the calculation of the mean first passage time. Also the higher eigenvalues for the relaxation decay modes in the case of ordinary Maier-Saupe potential are calculated. The results obtained are in full agreement with those of the approach developed by Coffey, Kalmykov, Déjardin and their coauthors in the whole range of barrier heights.
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