论文标题
Gibbs状态的量子自旋系统的经典限制
Classical limit of Gibbs states for quantum spin systems
论文作者
论文摘要
我们研究具有自旋量子数$ s $的自旋系统的量子机械和经典吉布斯状态之间的关系。众所周知，量子状态和可观测值可以由相位空间$ {\ Mathcal s} $上定义的函数表示，在我们的情况下，这是单位球体的$ n $折叠产品。因此，（适当缩放）量子gibbs状态的经典限制$ s \ to \ infty $可以描述为$ {\ Mathcal s} $上定义的函数限制。我们选择通过$ n $的多项式来近似哈密顿量的指数功能，因此必须处理在摩尔 - 奥斯古德定理中处理的双序列极限（取决于$ n $和$ s $）的极限问题。海森堡二聚体的示例说明了量子吉布斯态与经典的量子状态的收敛性。我们将我们的方法应用于描述旋转单元的相位空间函数的明确计算，并最终对自旋相干态的理论添加了一些一般性评论。
We study the relation between quantum mechanical and classical Gibbs states of spin systems with spin quantum number $s$. It is known that quantum states and observables can be represented by functions defined on the phase space ${\mathcal S}$, which in our case is the $N$-fold product of unit spheres. Therefore, the classical limit $s\to\infty$ of (suitably scaled) quantum Gibbs states can be described as the limit of functions defined on ${\mathcal S}$. We choose to approximate the exponential function of the Hamiltonian by a polynomial of degree $n$ and thus have to deal with the problem of the limit of double sequences (depending on $n$ and $s$) treated in the theorem of Moore-Osgood. The convergence of quantum Gibbs states to classical ones is illustrated by the example of the Heisenberg dimer. We apply our method to the explicit calculation of the phase space function describing spin monomials, and finally add some general remarks on the theory of spin coherent states.
