自旋密度矩阵I：一般理论和精确主方程
The Spin Density Matrix I: General Theory and Exact Master Equations
摘要：
我们考虑这样一种情况，即限制在量子点（QD）中的相互作用电子要么太接近而无法分辨，要么我们不希望应用解决它们的测量。然后，物理可观察到的是电子自旋（不能明确地归因于量子点的自旋）和系统状态完全描述的自旋密度矩阵。占的空间自由度，我们研究在何种程度上的哈密顿描述的自旋自由度是有效的。我们表明，只要单重态和三重态之间没有耦合，情况确实如此，但当存在这种耦合时，就会出现开放系统效应，即，即使没有与真实浴的相互作用，动力学也是非单一的。我们的主要重点是非幺正效应的调查，基于精确的主方程，我们推导出的自旋密度矩阵的Lindblad和无时间卷积（TCL）的形式，和量子计算的影响。特别是，我们证明了海森堡相互作用不影响幺正部分（除了兰姆位移），但影响非幺正贡献的自旋密度矩阵的时间演化。在后续的论文中，我们提出了一个详细的分析的两个量子点的示例系统，包括自旋轨道效应。
英文摘要：
We consider a scenario where interacting electrons confined in quantum dots (QDs) are either too close to be resolved, or we do not wish to apply measurements that resolve them. Then the physical observable is an electron spin only (one cannot unambiguously ascribe a spin to a QD) and the system state is fully described by the spin-density matrix. Accounting for the spatial degrees of freedom, we examine to what extent a Hamiltonian description of the spin-only degrees of freedom is valid. We show that as long as there is no coupling between singlet and triplet states this is indeed the case, but when there is such a coupling there are open systems effects, i.e., the dynamics is non-unitary even without interaction with a true bath. Our primary focus is an investigation of non-unitary effects, based on exact master equations we derive for the spin-density matrix in the Lindblad and time-convolutionless (TCL) forms, and the implications for quantum computation. In particular, we demonstrate that the Heisenberg interaction does not affect the unitary part (apart from a Lamb shift) but does affect the non-unitary contributions to time evolution of the spin-density matrix. In a sequel paper we present a detailed analysis of an example system of two quantum dots, including spin-orbit effects.
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