MARKOV STATES AND CHAINS ON THE CAR ALGEBRA
MARKOV STATES AND CHAINS ON THE CAR ALGEBRA
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汽车代数上的马尔可夫状态和链
DOI：
10.1142/s0219025707002683
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发表时间：
2007
期刊：
影响因子：
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通讯作者：
F. Mukhamedov
中科院分区：
文献类型：
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作者：
L. Accardi;F. Fidaleo;F. Mukhamedov
我们在ℤ上的正则反对易关系代数上引入了马氏态和马氏链的概念，强调了它与无限张量积情形的一些显著区别。我们描述了该代数上马氏态的结构，并证明了与无限张量积情形相反，并非所有这些状态都是可对角化的。给出了构造汽车代数上非平凡量子马氏链的一般方法，并用一些关键的例子加以说明。这一分析为量子马尔可夫过程的令人满意的理论提供了进一步的步骤。
We introduce the notion of Markov states and chains on the Canonical Anticommutation Relations algebra over ℤ, emphasizing some remarkable differences with the infinite tensor product case. We describe the structure of the Markov states on this algebra and show that, contrarily to the infinite tensor product case, not all these states are diagonalizable. A general method to construct nontrivial quantum Markov chains on the CAR algebra is also proposed and illustrated by some pivotal examples. This analysis provides a further step for a satisfactory theory of quantum Markov processes.