微非理想气体中的BBGKY方程、自扩散和1/f噪声
BBGKY equations, self-diffusion and 1/f noise in a slightly nonideal gas
摘要：
"分子混沌"的假设在应用于低密度气体的空间不均匀演化时失败，因为这一假设与将气体粒子的相互作用还原为"碰撞"是不相容的。分子混沌的失效意味着位形空间中相互碰撞的、紧密排列的粒子之间存在统计关联。如果考虑到这一事实，那么在碰撞近似中（在气体演化的动力学阶段），在无限小气体参数的极限下，Bogolyubov-Born-Green-Kirkwood-Yvon（BBGKY）方程族产生了一个自治的动力学方程组，用于紧密排列的粒子的多粒子分布函数。这个方程组只能在齐次情况下产生玻尔兹曼方程。用它来分析气体粒子的布朗运动的统计特性。分析表明，任何粒子的扩散率和迁移率都存在1/f谱的涨落。这些波动的物理原因是粒子相遇在碰撞参量值上的分布的随机性，并且因此是碰撞的速率和效率的随机性。本质上，这是{\bf reprint}在[Zh. Eksp. Teor.菲兹{\bf 94}（12），140 - 156（1988年12月）]并在[Sov.物理JETP {\bf 67}（12），469 - 2477（1988年12月）]，但似乎仍然未知的那些人可能是非常有用的。脚注载有目前增加的评论。
英文摘要：
The hypothesis of ``molecular chaos'' is shown to fail when applied to spatially inhomogeneous evolution of a low-density gas, because this hypothesis is incompatible with reduction of interactions of gas particles to ``collisions''. The failure of molecular chaos means existence of statistical correlations between colliding and closely spaced particles in configuration space. If this fact is taken into account, then in the collisional approximation (in the kinetic stage of gas evolution) in the limit of infinitely small gas parameter the Bogolyubov-Born-Green-Kirkwood-Yvon (BBGKY) hierarchy of equations yields an autonomous system of kinetic equations for the many-particle distribution functions of closely spaced particles. This system of equations can produce the Boltzmann equation only in the homogeneous case. It is used to analyze statistical properties of Brownian motion of a test gas particle. The analysis shows that there exist fluctuations with a 1/f spectrum in the diffusivity and mobility of any particle. The physical cause of these fluctuations is randomness of distribution of particles' encounters over the impact parameter values and, consequently, randomness of the rate and efficiency of collisions. In essence, this is {\bf reprint} of the like author's paper published in Russian in [ Zh. Eksp. Teor. Fiz. {\bf 94} (12), 140-156 (Dec. 1988)] and translated into English in [ Sov. Phys. JETP {\bf 67} (12), 469-2477 (Dec. 1988)] twenty years ago but seemingly still unknown to those to whom it might be very useful. The footnotes contain presently added comments.
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