Ghodrat Malihe, Montakhab Afshin
Department of Physics, College of Sciences, Shiraz University, Shiraz 71454, Iran.
Phys Rev E Stat Nonlin Soft Matter Phys. 2010 Jul;82(1 Pt 1):011110. doi: 10.1103/PhysRevE.82.011110. Epub 2010 Jul 8.
In this paper we consider the effect of different time parametrizations on the stationary velocity distribution function for a relativistic gas. We clarify the distinction between two such distributions, namely, the Jüttner and the Modified Jüttner distributions. Using a recently proposed model of a relativistic gas, we show that the obtained results for the proper-time averaging does not lead to the Modified Jüttner distribution (as recently conjectured), but introduces a Lorentz factor γ(v) (i.e., energy) to the well-known Jüttner function which results from observer-time averaging. These two modifications (i.e., Modified Jüttner function or Jüttner divided by energy) are identical in the rest frame; however, their distinction comes to light when one considers a moving frame. We obtain results for rest frame as well as moving frame in order to support our claim. We finally conclude that reparametrizing time simply rescales stationary (Jüttner) distribution function according to a well-defined frame-independent relation.
在本文中，我们考虑了不同时间参数化对相对论气体静止速度分布函数的影响。我们阐明了两种这样的分布之间的区别，即尤特纳分布和修正尤特纳分布。使用最近提出的相对论气体模型，我们表明，对于原时平均所获得的结果不会导致修正尤特纳分布（如最近所推测的那样），而是将一个洛伦兹因子γ(v)（即能量）引入到由观测者时间平均产生的著名的尤特纳函数中。这两种修正（即修正尤特纳函数或尤特纳函数除以能量）在静止参考系中是相同的；然而，当考虑一个运动参考系时，它们的区别就显现出来了。为了支持我们的观点，我们得到了静止参考系和运动参考系的结果。我们最终得出结论，重新参数化时间只是根据一个明确的与参考系无关的关系对静止（尤特纳）分布函数进行重新缩放。
