Starting from the Liouville's equation, we have derived an expression for the electrical current and a boltzmann-type equation for diagonal elements of the density matrix in the lowest order of the electron-phonon interaction. 针对低补偿情况,略去复杂能带结构,我们由刘维方程出发,把密度矩阵对电场,然后对电声子作用展开,得到电流表达式及密度矩阵对角元所满足的玻兹曼型方程。
Applying BBGKY equation obtained from Liouville's equation to a system with many components, the irreversible chemical reaction-diffusion equation can be deduced. 把由刘维方程推得的BBGKY方程用于多元系,可导出不可逆化学反应扩散方程。
The Backlund Transformation and Nonlinear Superposition Formula of Solutions for the Liouville's Equation in Higher Dimensions 关于高维Liouville方程的Backlund变换和解的非线性叠加公式