李群上的布朗运动与开放量子系统
Brownian motion on Lie groups and open quantum systems
摘要：
我们研究旋转半群的（超）运营商，即某些量子动力学半群相关联的，在一个自然的方式，与对形成的投影表示的局部紧群和卷积半群的概率措施在这个群体。阐明了这类算子半群与（经典）布朗运动之间的联系。证明了每个与有限维表示相关联的旋转半群都是随机酉半群，反过来，每个随机酉半群都是旋转半群。使用标准工具的卷积半群的措施和凸分析的理论，我们提供了一个完整的表征旋转半群与有限维酉表示的李群的无穷小生成元。
英文摘要：
We study the twirling semigroups of (super)operators, namely, certain quantum dynamical semigroups that are associated, in a natural way, with the pairs formed by a projective representation of a locally compact group and a convolution semigroup of probability measures on this group. The link connecting this class of semigroups of operators with (classical) Brownian motion is clarified. It turns out that every twirling semigroup associated with a finite-dimensional representation is a random unitary semigroup, and, conversely, every random unitary semigroup arises as a twirling semigroup. Using standard tools of the theory of convolution semigroups of measures and of convex analysis, we provide a complete characterization of the infinitesimal generator of a twirling semigroup associated with a finite-dimensional unitary representation of a Lie group.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
