纯归纳极限态与Kolmogorov性质
Pure inductive limit state and Kolmogorov's property
摘要：
设$(\clb,λ_t,ψ)$是一个$C^*$ -动力系统，其中$(λ_t: t \in \IT_+)$是一个内射自同态半群，$ψ$是$C^*$子代数$\clb$上的一个$(λ_t)$不变状态，$\IT_+$是非负整数或实数.本论述的中心目的是找到一个有用的标准，归纳极限状态$\clb \raro^{λ_t} \clb$规范与$ψ$是纯的。我们实现这一点，通过探索最小弱向前和向后马尔可夫过程与马尔可夫半群的支持投影的状态$ψ$的角落冯-诺伊曼代数证明，Kolmogorov的性质[Mo 2]的马尔可夫半群是一个充分条件的诱导状态是纯的。作为这个判据的应用，我们找到了一维量子自旋链上的平移不变因子态是纯态的一个充分条件。这个标准在某种意义上补充了[BJKW，Mo 2]中得到的标准，因为我们可以超越晶格对称态。
英文摘要：
Let $(\clb,λ_t,ψ)$ be a $C^*$-dynamical system where $(λ_t: t \in \IT_+)$ be a semigroup of injective endomorphism and $ψ$ be an $(λ_t)$ invariant state on the $C^*$ subalgebra $\clb$ and $\IT_+$ is either non-negative integers or real numbers. The central aim of this exposition is to find a useful criteria for the inductive limit state $\clb \raro^{λ_t} \clb$ canonically associated with $ψ$ to be pure. We achieve this by exploring the minimal weak forward and backward Markov processes associated with the Markov semigroup on the corner von-Neumann algebra of the support projection of the state $ψ$ to prove that Kolmogorov's property [Mo2] of the Markov semigroup is a sufficient condition for the inductive state to be pure. As an application of this criteria we find a sufficient condition for a translation invariant factor state on a one dimensional quantum spin chain to be pure. This criteria in a sense complements criteria obtained in [BJKW,Mo2] as we could go beyond lattice symmetric states.
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。
