论文标题
在具有不变亚词架的量子动力学半群的发电机上
On the generators of quantum dynamical semigroups with invariant subalgebras
论文作者
论文摘要
文献中不同的姿态出现了以不变的形式表征GKLS发电机和CP映射的问题。我们证明了两个统一的结果，这些结果甚至适用于弱闭合的 *-algebras：首先，我们展示了如何为$ \ Mathcal {a} $ - 不变的GKLS-generators构造正常形式，如果$ \ nathcal {a} $ - 不变的cp-maps的普通形式，则已知 - 已知两种问题，这是两个问题。其次，如果$ \ Mathcal {a} $是原子（其中包括有限维情况），我们为$ \ Mathcal {a} $ - 不变的CP-MAPS提供正常形式。作为应用程序，我们将文献的几个结果重现为我们的特征的直接后果，从而指出了不同字段之间的联系。
The problem of characterizing GKLS-generators and CP-maps with an invariant appeared in different guises in the literature. We prove two unifying results which hold even for weakly closed *-algebras: First, we show how to construct a normal form for $\mathcal{A}$-invariant GKLS-generators, if a normal form for $\mathcal{A}$-invariant CP-maps is known - rendering the two problems essentially equivalent. Second, we provide a normal form for $\mathcal{A}$-invariant CP-maps if $\mathcal{A}$ is atomic (which includes the finite-dimensional case). As an application we reproduce several results from the literature as direct consequences of our characterizations and thereby point out connections between different fields.
