论文标题
可集成的（古典和量子）四波混合哈密顿系统
An integrable (classical and quantum) four-wave mixing Hamiltonian system
论文作者
论文摘要
研究了在经典和量子水平上的四波混合哈密顿系统。在经典情况下，如果假设表格的频率共振条件$ω_0-Ω_1 +ω_2-Ω_____________________3= 0 $，则该哈密顿系统将集成在四倍元中，并且提出了解决方案的显式公式。在相同的条件下，发现了量子哈密顿量的光谱分解，因此，该系统的Heisenberg方程被求解。在非线性光学元件中获得的结果的某些应用被剥夺了。
A four-wave mixing Hamiltonian system on the classical as well as on the quantum level is investigated. In the classical case, if one assumes the frequency resonance condition of the form $ω_0 -ω_1 +ω_2 -ω_3=0$, this Hamiltonian system is integrated in quadratures and the explicit formulas of solutions are presented. Under the same condition the spectral decomposition of quantum Hamiltonian is found and thus, the Heisenberg equation for this system is solved. Some applications of the obtained results in non-linear optics are disscused.
