论文标题
高斯国家进化的差分参数形式主义：非整体进化和不变状态
Differential Parametric Formalism for the Evolution of Gaussian States: Nonunitary Evolution and Invariant States
论文作者
论文摘要
在详细阐述的差异方法中，我们研究了高斯，混合，连续可变密度矩阵的参数的演变，其动力学是由赫米尔顿汉密尔顿人给出的，这些动力学以二次形式的位置和动量算子或正交成分的二次形式。具体而言，我们以通用形式获得协方差矩阵的微分方程，平均值和多部分高斯状态的密度矩阵参数，根据汉密尔顿$ \ hat {h} $的单位演变。我们还提出了描述子系统非正式演化的相应微分方程。所得的非线性方程用于求解系统的动力学，而不是schrödinger方程。形式主义阐述使我们能够定义新的特定不变和准不变状态，以及具有不变协方差矩阵的状态，即，状态仅是根据古典汉密尔顿方程而演变的平均值。通过在位置和断层概率表示中使用密度矩阵，我们研究了这些特性的示例。作为示例，我们为两部分参数放大器的两模式转换器和准不变态提供了新颖的状态。
In a differential approach elaborated, we study the evolution of the parameters of Gaussian, mixed, continuous variable density matrices, whose dynamics are given by Hermitian Hamiltonians expressed as quadratic forms of the position and momentum operators or quadrature components. Specifically, we obtain in generic form the differential equations for the covariance matrix, the mean values, and the density matrix parameters of a multipartite Gaussian state, unitarily evolving according to a Hamiltonian $\hat{H}$. We also present the corresponding differential equations which describe the nonunitary evolution of the subsystems. The resulting nonlinear equations are used to solve the dynamics of the system instead of the Schrödinger equation. The formalism elaborated allows us to define new specific invariant and quasi-invariant states, as well as states with invariant covariance matrices, i.e., states were only the mean values evolve according to the classical Hamilton equations. By using density matrices in the position and in the tomographic-probability representations, we study examples of these properties. As examples, we present novel invariant states for the two-mode frequency converter and quasi-invariant states for the bipartite parametric amplifier.
