Levitt Malcolm H, Bengs Christian
School of Chemistry, University of Southampton, SO17 1BJ, Southampton, UK.
Magn Reson (Gott). 2021 Jun 8;2(1):395-407. doi: 10.5194/mr-2-395-2021. eCollection 2021.
The quantum state of a spin ensemble is described by a density operator, which corresponds to a point in the Liouville space of orthogonal spin operators. Valid density operators are confined to a particular region of Liouville space, which we call the physical region and which is bounded by multidimensional figures called simplexes. Each vertex of a simplex corresponds to a pure-state density operator. We provide examples for spins , , and for coupled pairs of spins-1/2. We use the von Neumann entropy as a criterion for hyperpolarization. It is shown that the inhomogeneous master equation for spin dynamics leads to non-physical results in some cases, a problem that may be avoided by using the Lindbladian master equation.
自旋系综的量子态由一个密度算符描述，该密度算符对应于正交自旋算符的刘维尔空间中的一个点。有效的密度算符被限制在刘维尔空间的一个特定区域，我们称之为物理区域，它由称为单纯形的多维图形界定。单纯形的每个顶点对应一个纯态密度算符。我们给出了自旋1、自旋1/2以及自旋1/2耦合对的例子。我们使用冯·诺依曼熵作为超极化的判据。结果表明，自旋动力学的非齐次主方程在某些情况下会导致非物理结果，这个问题可以通过使用林德布拉德主方程来避免。
