狭义相对论中的扩散
Diffusion in the special theory of relativity
摘要：
马尔可夫扩散理论是在狭义相对论的框架内推广的，使用黎曼流形（具有确定度量）上扩散的数学演算的修改来描述具有不确定度量的洛伦兹流形上的扩散。本文定义了位置、速度和正交速度坐标系纤维空间中的广义Langevin方程，由此导出了相空间中外力场中的广义相对论Kramers方程。所得到的扩散方程在洛伦兹变换下是不变的，其定态解由Jüttner分布给出。此外，还以相对论性无力扩散为例导出了非定常解析解。
英文摘要：
The Markovian diffusion theory is generalized within the framework of the special theory of relativity using a modification of the mathematical calculus of diffusion on Riemannian manifolds (with definite metric) to describe diffusion on Lorentzian manifolds with an indefinite metric. A generalized Langevin equation in the fiber space of position, velocity and orthonormal velocity frames is defined from which the generalized relativistic Kramers equation in the phase space in external force fields is derived. The obtained diffusion equation is invariant under Lorentz transformations and its stationary solution is given by the Jüttner distribution. Besides a non-stationary analytical solution is derived for the example of force-free relativistic diffusion.
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