时间平移

用时间平移矩阵方法对真空中V型三能级原子非线性光学性质的理论研究

Theoretical studies of nonlinear properties for V-level atoms in vacuum by using time translational matrix method

运用时间平移矩阵研究了真空中V型三能级原子在外场作用下的非线性光学性质，具体推导了三阶偶极跃迁矩阵元随时间演化规律。

The nonlinear properties of V level atoms in vacuum under the action of external optical fields was studied by time translational matrix method .

文章首先得到了时间平移样本在混叠效应中的能量叠加性质，并在此性质的基础上，提出了一个离散傅里叶变换算法，CRSS算法。

The properties of time-shifted samples in aliasing effects are obtained first . Based on the properties , we provide a discrete Fourier transform algorithm , CRSS algorithm .

在时间平移下的不变性导致能量守恒。

Invariance under translation in time leads to conservation of energy .

时间平移对称性与能量守恒

Time translation symmetry and conservation of energy

其中着重讨论它们的平移特性，由此导出双粒子的时间平移算子。

By constructing different singular functions , their properties , especially , their displacement properties are discussed , from which the time-displacement operators of Two-particles are derived .

从对称性原理出发，证明了能量守恒定律，并对时间平移对称性与能量守恒作了简单的几何表述。

From the principle of symmetry , law of conservation of energy is proved . And have a simple geometric express for time translation symmetry and conservation of energy .

通过一个沿时间轴平移的观察窗，观察时间进程中时间序列各演化模式相对概率的变化情况，捕捉其蕴含的时间信息。

Through a sliding observation window , the relative probability of EPs of a time series can be monitored as a function of time .

关键词：时间和空间平移对称性；时间反演对称性；守恒律；对称破缺。

KEY WORDS : time and space translation symmetry ; time reversal symmetry ; conservation law ; symmetry breaking .

最后，因为没有绝对的时间原点，所以任何系统在时间平移下一定不变。

Finally , since there is no absolute origin in time , all systems must be invariant under time displacements .