费米马尔可夫态
Fermi Markov states
摘要：
研究了一般费米子代数上的马尔可夫态的结构。在本文件中处理的情况涵盖，除了d-马尔可夫状态的CAR代数Z（即当有d-零化子和创造者在每个网站上），也是非齐次的情况下（即当发电机的数量取决于本地化）。本分析提供了第一个必要的步骤的一般性质的研究，并建设非平凡的例子费米马尔可夫状态的d-标准格，即费米马尔可夫场。详细研究了KMS边界条件与费米马尔可夫态熵之间的自然联系。除了一类与张量积代数中出现的状态非常相似的马尔可夫态（在续集中称为“强偶”）之外，费米马尔可夫态的其他有趣的例子自然也会出现。与强偶的例子不同，后者是高度纠缠的，预计它们描述的相互作用不是“交换最近邻”。因此，非强偶马尔可夫态除了在量子统计力学中的自然应用外，在信息论中也可能是有意义的。
英文摘要：
We investigate the structure of the Markov states on general Fermion algebras. The situation treated in the present paper covers, beyond the d--Markov states on the CAR algebra on Z (i.e. when there are d--annihilators and creators on each site), also the non homogeneous case (i.e. when the numbers of generators depends on the localization). The present analysis provides the first necessary step for the study of the general properties, and the construction of nontrivial examples of Fermi Markov states on the d--standard lattice, that is the Fermi Markov fields. Natural connections with the KMS boundary condition and entropy of Fermi Markov states are studied in detail. Apart from a class of Markov states quite similar to those arising in the tensor product algebras (called "strongly even" in the sequel), other interesting examples of Fermi Markov states naturally appear. Contrarily to the strongly even examples, the latter are highly entangled and it is expected that they describe interactions which are not "commuting nearest neighbor". Therefore, the non strongly even Markov states, in addition to the natural applications to quantum statistical mechanics, might be of interest for the information theory as well.
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