论文标题
痕量类操作员的模块化结构以及无限退化系统的动力学平衡状态的应用
Modular Structures on Trace Class Operators and Applications to Themodynamical Equilibrium States of Infinitely Degenerate Systems
论文作者
论文摘要
我们研究了无限退化的哈密顿人的热平衡状态（KMS状态），我们研究了Landau水平的例子。我们将所有KMS状态分类为适合描述无限退化系统的代数示例，我们表明没有循环和分离的向量与Landau Hamiltonian相对应。然后，我们试图重现Haag Hugenholtz和Winnink的KMS State理论开始时使用的有限盒子的热力学极限。最后，我们从非 - $σ$ - addive概率，非正常状态或半限定状态，单数（dixmier）状态的角度讨论了情况，因此，kms状态的概念的扩展。
We study the thermal equilibrium states (KMS states) of infinitely degenerate Hamiltonians, in particular, we study the example of the Landau levels. We classify all KMS states in an example of algebra suitable for describing infinitely degenerate systems and we show that there is no cyclic and separating vector corresponding to the Landau Hamiltonian. Then, we try to reproduce the thermodynamical limit of a finite box as used in the very beginning of the theory of KMS states by Haag Hugenholtz and Winnink. Finally, we discuss the situation from the point of view of non-$σ$-additive probabilities, non-normal nor semifinite states, singular (Dixmier) states and, hence, an extension of the concept of KMS state.
