论文标题
平衡经典多粒子系统和广义线性玻尔兹曼和兰道方程中波动的亚动力学
Subdynamics of fluctuations in an equilibrium classical many-particle system and generalized linear Boltzmann and Landau equations
论文作者
论文摘要
新的精确封闭的均匀均匀的总体方程式（GME），在平衡两次相关函数中的演变，用于从n >> 1个经典多体系统的N >> 1个粒子中选择的动态变量的动态变量，从gme）由于没有不均匀的术语，该术语在最初的时间时刻包含所有n个粒子之间的相关性，并防止了S粒子子系统演变的闭合描述。描述波动亚动力学的封闭均匀的GME是通过将特殊的投影操作员应用于管理N颗粒系统动力学的Liouville方程中获得的。在颗粒密度的线性近似中，在所有时间尺度上都有线性广义玻尔兹曼方程，并且在所有时间尺度上都有效，对于弱粒子间相互作用，该方程将转换为广义的线性Landau方程，在该方程中，在该方程中，也可以考虑初始相关性。讨论了这些方程与非线性玻尔兹曼和兰道方程的连接。
New exact completely closed homogeneous Generalized Master Equations (GMEs), governing the evolution in time of equilibrium two-time correlation functions for dynamic variables of a subsystem of s particles (s<N) selected from N>>1 particles of a classical many-body system, are obtained These time-convolution and time-convolutionless GMEs differ from the known GMEs (e.g. Nakajima-Zwanzig GME) by absence of inhomogeneous terms containing correlations between all N particles at the initial moment of time and preventing the closed description of s-particles subsystem evolution. Closed homogeneous GMEs describing the subdynamics of fluctuations are obtained by applying a special projection operator to the Liouville equation governing the dynamics of N-particle system. In the linear approximation in the particles' density, the linear Generalized Boltzmann equation accounting for initial correlations and valid at all timescales is obtained This equation for a weak inter-particle interaction converts into the generalized linear Landau equation in which the initial correlations are also accounted for. Connection of these equations to the nonlinear Boltzmann and Landau equations are discussed.
