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arXiv 1908.02017cond-mat.stat-mech
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受外力驱动的多粒子经典系统从平衡态出发的子动力学

Subdynamics of a many-particle classical system driven from an equilibrium state by an external force

Victor Los

摘要:

本文证明,通过一个特殊的投影算子,经典粒子的N粒子分布函数的Liouville方程,在外场的驱动下,可以精确地转化为s粒子(s<N)分布函数的封闭的线性齐次广义主方程。所得到的线性时间卷积和无时间卷积的广义相对论在s粒子相空间中定义了一个子动力学,与传统的广义相对论相比,不包含非齐次的初始相关项。不需要像“分子混沌”或博戈留波夫的减弱初始相关性的原理那样的近似。初始相关性被“隐藏”在投影算子中,因此它们在所获得的方程中被考虑。对于弱粒子间相互作用和弱外场,这些方程被改写为二阶微扰理论。从本质上讲,它们包含了初始相关性在控制s粒子分布函数演化的内核中的贡献。特别地,得到了单粒子分布函数的演化方程,并讨论了它与非线性朗道方程和福克-普朗克方程的关系。所得结果与统计物理的一般问题和物理应用(等离子体物理)有关。

英文摘要:

It is shown, that by means of a special projection operator, the Liouville equation for an N-particle distribution function of classical particles, driven from an equilibrium state by an external field, can be exactly converted into a closed linear homogeneous Generalized Master Equations (GMEs) for an s-particle (s<N) distribution function. The obtained linear time-convolution and time-convolutionless GMEs define a subdynamics in the s-particle phase space and contains no inhomogeneous initial correlations terms as compared to the conventional GMEs. No approximation like "molecular chaos" or Bogoliubov's principle of weakening of initial correlations is needed. The initial correlations are "hidden" in the projection operator and thus they are accounted for in the obtained equations. For the weak interparticle interaction and weak external field, these equations are rewritten in the second order of the perturbation theory. Essentially, that they contain the contribution of initial correlations in the kernel governing the evolution of an s-particle distribution function. In particular, the evolution equation for a one-particle distribution function is obtained and its connection to the nonlinear Landau and the Fokker-Planck equations is discussed. The obtained results are related to the general issues of statistical physics and to the physical applications (plasma physics).

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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