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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Maxwell–Jüttner distribution ： ウィキペディア英語版 Maxwell–Jüttner distribution In physics, the Maxwell–Jüttner distribution is the distribution of speeds of particles in a hypothetical gas of relativistic particles. Similar to Maxwell's distribution, the Maxwell–Jüttner distribution considers a classical ideal gas where the particles are dilute and do not significantly interact with each other. The distinction from Maxwell's case is that effects of special relativity are taken into account. In the limit of low temperatures ''T'' much less than ''mc''2/''k'' (where ''m'' is the mass of the kind of particle making up the gas, ''c'' is the speed of light and ''k'' is Boltzmann's constant), this distribution becomes identical to the Maxwell–Boltzmann distribution. The distribution can be attributed to Ferencz Jüttner, who derived it in 1911. It has become known as the Maxwell–Jüttner distribution by analogy to the name Maxwell-Boltzmann distribution that is commonly used to refer to Maxwell's distribution. ==The distribution function == As the gas becomes hotter and ''kT'' approaches or exceeds ''mc''2, the probability distribution for $\backslash gamma=1/\backslash sqrt$ in this relativistic Maxwellian gas is given by the Maxwell–Jüttner distribution:〔 〕 :$f(\backslash gamma)\; =\; \backslash frac$ \exp \left( - \frac \right) where $\backslash beta\; =\; \backslash frac\; =\backslash sqrt,$ $\backslash theta=\backslash frac,$ and $K\_2$ is the modified Bessel function of the second kind. Alternatively, this can be written in terms of the momentum as :$f(\backslash mathbf)\; =\; \backslash frac\; \backslash exp\backslash left(\; -\backslash frac\backslash right)$ where $\backslash gamma(p)\; =\; \backslash sqrt\backslash right)^2\}$. The Maxwell–Jüttner equation is covariant, but not manifestly so, and the temperature of the gas does not vary with the gross speed of the gas. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Maxwell–Jüttner distribution」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.