物态方程曲面上临界点高斯曲率的物理意义

PHYSICAL SIGNIFICANCE OF GAUSSIAN CURVATURE AT CRITICAL POINTS OF EQUATION OF STATE SURFACES

物态方程曲面在临界点的高斯曲率为零与否,完全由压缩率临界指数确定。根据微分几何中高斯曲率-局部曲面形状之间的关系,可以推知一个高斯曲率-临界指数关系:相变点两侧的压缩率临界指数只有两种情况,都等于1或者同时大于1。作为高斯曲率-临界指数关系的一个检验,我们直接计算理想玻色气体物态方程曲面在临界点的高斯曲率,发现临界指数大于1,这一点和实验结果相符。

Whether the Gaussian curvature of the equation of state surface at the critical pointdiffers from zero is completely determined by the compressibility critical exponent. According to the relationship between the Gaussian curvature-local shape of the surface in differential geometry, the local shape at a point on the surface is determined by the Gaussian curvature. It can then be inferred that there are only two cases of the critical exponent. The critical exponents on both sides of the phase transition point are equal to 1 or greater than 1. Bose-Einstein condensation of free Bose gas is utilized to illustrate the general result between the Gaussian curvature and the critical exponent.