Results are presented for the conservation laws (CLs) for the optical Bloch equations (OBEs) for the Λ scheme under action of two light fields. The method of multipliers (variational derivative method) is used to obtain CLs which are dependent on the density-matrix elements. Results are classified and discussed by the phenomenological parameters and processes characteristic for OBEs, like the relaxation and decoherence, and the detunings of light fields. CLs for the Liouville von Neumann equation, as a special case of OBEs, without relaxation and decoherence terms, are presented and it is shown that traces, characteristic polynomials and their coefficients, eigen-values and determinants of class of matrices represent CLs. We also presented method, which used CLs obtained by the method of multipliers, to construct another set of CLs, which have the explicit time dependence and are valid for the larger set of parameters, with relaxation due to time of flight and spontaneous emissi...

中文翻译：

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Λ方案的光学Bloch方程的守恒律

给出了在两个光场作用下Λ方案的光学Bloch方程（OBE）的守恒律（CL）的结果。乘数法（变分微分法）用于获得依赖于密度矩阵元素的CL。通过OBE的现象学参数和过程特征（如弛豫和退相干以及光场的失谐）对结果进行分类和讨论。介绍了作为OBE的特例的Liouville von Neumann方程的CL，没有松弛和退相干项，并且表明，迹线，特征多项式及其系数，特征值和矩阵类别的行列式表示CL。我们还提出了一种方法，该方法使用通过乘法器方法获得的CL来构建另一组CL，