An extension of the Kac ring model
An extension of the Kac ring model
复制标题
Kac环模型的扩展
DOI：
10.1088/0305-4470/36/46/001
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发表时间：
2003
期刊：
影响因子：
--
通讯作者：
K. Netočný
中科院分区：
文献类型：
--
作者：
W. Roeck;Tim Jacobs;Christian Maes;K. Netočný
我们引入了量子自旋的酉动力学，这是 Mark Kac 为阐明弛豫到平衡现象而引入的模型的扩展。当自旋数量变得非常大时，磁化强度满足作为时间函数的自主方程，并以指数方式快速弛豫到由微正则系综确定的平衡磁化强度。这被证明为关于一类初始数据的大数定律。还计算了相应的吉布斯-冯·诺依曼熵并讨论了其时间单调性。
We introduce a unitary dynamics for quantum spins which is an extension of a model introduced by Mark Kac to clarify the phenomenon of relaxation to equilibrium. When the number of spins becomes very large, the magnetization satisfies an autonomous equation as a function of time with exponentially fast relaxation to the equilibrium magnetization as determined by the microcanonical ensemble. This is proved as a law of large numbers with respect to a class of initial data. The corresponding Gibbs-von Neumann entropy is also computed and its monotonicity in time discussed.