论文标题
具有多个自由度的量子系统的确切马尔可夫的演变：相空间表示
Exact Markovian evolution of quantum systems with several degrees of freedom : Phase space representations
论文作者
论文摘要
用二次哈密顿量和线性耦合算子的Lindblad方程的精确解在和弦表示内，即Wigner函数的傅立叶变换，也称为特征函数。它在这里已被概括为几个自由度，以便为任何子系统的降低密度运算符以及以这种不断发展的和弦函数的衍生物表示的矩提供明确的表达。 Wigner函数是其直接经典演化的卷积，具有扩大的多维高斯窗口，最终确保了其阳性。 futher，阳性也适用于Glauber-Sundarshan P功能，这可以确保组件的可分离性。在几个自由度的背景下，定义了一个完整的耗散矩阵，其痕迹等于先前衍生的耗散系数的两倍。这控制了Wigner函数参数合同的相位空间量的速率，而和弦函数的相位量则扩大。讨论了三位星分子和一系列谐波振荡器的马尔可夫进化的例子。
The exact solution of the Lindblad equation with a quadratic Hamiltonian and linear coupling operators was derived within the chord representation, that is, for the Fourier transform of the Wigner function, also known as the characteristic function. It is here generalized for several degrees of freedom, so as to provide an explicit expression for the reduced density operator of any subsystem, as well as moments expressed as derivatives of this evolving chord function. The Wigner function is then the convolution of its straightforward classical evolution with a widening multidimensional Gaussian window, eventually ensuring its positivity. Futher on, positivity also holds for the Glauber-Sundarshan P function, which guarantees separability of the components. In the context of several degrees of freedom, a full dissipation matrix is defined, whose trace is equal to twice the previously derived dissipation coefficient. This governs the rate at which the phase space volume of the argument of the Wigner function contracts, while that of the chord function expands. Examples of Markovian evolution of a triatomic molecule and of an array of harmonic oscillators are discussed.
