论文标题
在操作员空间II上的量子随机共生和完全有限的半群
Quantum stochastic cocycles and completely bounded semigroups on operator spaces II
论文作者
论文摘要
量子随机的共体为量子环境中的时间均匀的马尔可夫演变提供了一个基本模型，在Schrodinger和Heisenberg Pictures中，在连续时间进行量子随机步行的直接对应物提供了一个直接的对应模型。本文是续集的续集，其中在操作员空间或C*-Algebra上建立了对应关系，以及在操作员空间上关联的矩阵空间上的Schur-Action`global'半群的类别。在本文中，我们通过产生相应的全球半群来研究同伴的随机产生，其主要目的是增强半群理论对量子随机共生分析和构建的适用性范围。给出了完全有限的共生的随机发电机与其任何相关的全局半群的发生器之间的仿射关系的明确描述。使用此情况，在C* - 代数上完全积极的准量子量子循环循环的随机发生器的结构，其期望半群是规范性的，从而使Christensen-evans-Evans-Evans的全面随机概括gks＆l theorem gos＆l theorem of Gorini，kossakakowski and sudarshan和sudarshan和lindblad and lindblad and lindblad and lindblad and lindblad and lindblad and lindblad and lindblad。转换还为具有无界结构图作为随机发生器的Cocycles提供了新的存在定理。后者被应用于称为量子排除过程的相互作用粒子模型，尤其是在尺寸一和两个方面的整数晶格上。
Quantum stochastic cocycles provide a basic model for time-homogeneous Markovian evolutions in a quantum setting, and a direct counterpart in continuous time to quantum random walks, in both the Schrodinger and Heisenberg pictures. This paper is a sequel to one in which correspondences were established between classes of quantum stochastic cocycle on an operator space or C*-algebra, and classes of Schur-action `global' semigroup on associated matrix spaces over the operator space. In this paper we investigate the stochastic generation of cocycles via the generation of their corresponding global semigroups, with the primary purpose of strengthening the scope of applicability of semigroup theory to the analysis and construction of quantum stochastic cocycles. An explicit description is given of the affine relationship between the stochastic generator of a completely bounded cocycle and the generator of any one of its associated global semigroups. Using this, the structure of the stochastic generator of a completely positive quasicontractive quantum stochastic cocycle on a C*-algebra whose expectation semigroup is norm continuous is derived, giving a comprehensive stochastic generalisation of the Christensen--Evans extension of the GKS&L theorem of Gorini, Kossakowski and Sudarshan, and Lindblad. The transformation also provides a new existence theorem for cocycles with unbounded structure map as stochastic generator. The latter is applied to a model of interacting particles known as the quantum exclusion Markov process, in particular on integer lattices in dimensions one and two.
