论文标题
谐波振荡器的量子主方程的特征值
Eigenvalues of the Liouvillians of Quantum Master Equation for a Harmonic Oscillator
论文作者
论文摘要
谐波振荡器的马尔可维亚主方程式的特征值具有通用形式。所考虑的liouvillians在位置坐标或创建和歼灭操作员以及具有正重归一致的频率的位置是二次的。我们通过证明这种形式的通用liouvillian可以与Kossakowski-lindblad方程的Liouvillian相似，证明了这一点，该方程已经知道。通用liouvillian的左右本征函数也形成了完整的生物表达集。给出了类似相关的右征本征的示例。
The eigenvalues of the Liouvillians of Markovian master equation for a harmonic oscillator have a generic form. The Liouvillians considered are quadratic in the position coordinates or creation and annihilation operators, as well as having positive renormalized frequencies. We prove this by showing that a generic Liouvillian of this form can be similarly related to the Liouvillian of the Kossakowski--Lindblad equation, whose eigenvalues are already known. The left and right eigenfunctions of the generic Liouvillian also form a complete and biorthogonal set. Examples of similarly related right eigenfunctions are given.
