Voigt轮廓函数概率推广的演化方程
Evolution equations of the probabilistic generalization of the Voigt profile function
摘要：
在分子光谱学和大气辐射转移中出现的作为多普勒和压力加宽的组合效应的光谱轮廓被称为Voigt轮廓函数。由于其卷积积分表示，Voigt轮廓可以被解释为具有高斯密度（由于多普勒效应）和洛伦兹密度（由于压力效应）的两个独立随机变量之和的概率密度函数。由于这些密度属于对称Lévy稳定分布类，因此提出了两个任意对称Lévy密度的卷积的概率推广。我们研究的情况下，所考虑的分布的宽度取决于一个尺度因子$τ$，这是代表的空间不均匀性或时间非平稳性。本文引入了这种概率推广的Voigt函数的演化方程，并将其解释为含有两个Riesz空间分数阶导数的广义扩散方程，从而将其归类为二阶空间分数阶扩散方程。
英文摘要：
The spectrum profile that emerges in molecular spectroscopy and atmospheric radiative transfer as the combined effect of Doppler and pressure broadenings is known as the Voigt profile function. Because of its convolution integral representation, the Voigt profile can be interpreted as the probability density function of the sum of two independent random variables with Gaussian density (due to the Doppler effect) and Lorentzian density (due to the pressure effect). Since these densities belong to the class of symmetric Lévy stable distributions, a probabilistic generalization is proposed as the convolution of two arbitrary symmetric Lévy densities. We study the case when the widths of the considered distributions depend on a scale-factor $τ$ that is representative of spatial inhomogeneity or temporal non-stationarity. The evolution equations for this probabilistic generalization of the Voigt function are here introduced and interpreted as generalized diffusion equations containing two Riesz space-fractional derivatives, thus classified as space-fractional diffusion equations of double order.
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