发表机构
Enexis Group; Delft University of Technology; Leipzig University（Enexis集团; 代尔夫特理工大学; 莱比锡大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文刻画了KMS-对称量子马尔可夫半群生成元的微分结构，给出了有界与无界量子狄利克雷型用导数表示的完整描述，并揭示了模群在定义域上的强连续性及平方根的增生性。
AI 中文摘要
KMS-对称量子马尔可夫半群完全由其诱导在GNS希尔伯特空间上的二次型决定。以这种方式产生的二次型称为量子狄利克雷型。本文给出了有界量子狄利克雷型关于导数的完整描述。特别地，我们展示了类型I因子上有界量子狄利克雷型的显式刻画。我们还证明了任何无界量子狄利克雷型都可以用导数表示。关键的技术洞见是模群总是限制在量子狄利克雷型的定义域上成为一个强连续群，使得解析生成元的平方根关于型范数是增生的。
英文摘要
A KMS-symmetric quantum Markov semigroup is completely determined by the quadratic form in induces on the GNS Hilbert space. The quadratic forms that arise in this way are called quantum Dirichlet forms. In this article we give a complete description of bounded quantum Dirichlet forms in terms of derivations. In particular, we exhibit an explicit characterization of the bounded quantum Dirichlet forms on type I factors. We also show that any unbounded quantum Dirichlet form can be represented in terms of derivations. The key technical insight is that the modular group always restricts to a strongly continuous group on the domain of a quantum Dirichlet form such that the square root of the analytic generator is accretive with respect to the form norm.
