相对论修正对麦克斯韦-玻耳兹曼分布律的影响

EFFECT OF RELATIVISTIC CORRECTION ON MAXWELL-BOLTZMANN DISTRIBUTION LAW

在本文中,分别推导了低速情形(E≈m_0c^2+p^2/2m_0)和一般情形(E=p^2c^2+m0~2c^4)下考虑相对论修正的动量分布表达式和速率分布表达式,发现低速情形下修正后的动量分布形式与不考虑修正的动量分布在形式上一致,而速率分布形式发生了改变;对一般情形的动量分布函数和速率分布函数进行了数值模拟并对结果进行了必要讨论.我们发现当β减少时整个动量分布曲线向大动量区域延伸,当β较大,即温度较低使得p<1时,一般情形将近似为低速情形.

In this paper, the momentum spectrum function （MSF） and the speed distribution function （SDF） which are taken account of relativity corrections at low speed situation and general situation have been deduced, respectively. It has been found that the form of the modified MSF at low speed situation is same as the one without being corrected, while there are much differences between the modified SDF and the one without being corrected at low speed situation; we have carried out numerical simulation to the MSF and the SDF at general situation with mathematic, and made a necessary discussion to the results. As the parameter β reduces, the case that the momentum spectrum will extend to the big momentum direction was discovered. While the parameter β becomes big enough to make the p〈1, the MSF at general situation will approximate to the one at low speed situation.