论文标题
两类混合古典量子动力学
The two classes of hybrid classical-quantum dynamics
论文作者
论文摘要
量子系统和经典系统之间的耦合是一致的，只要在状态空间中的演化是线性的，将系统的拆分保留为量子和经典的自由度，并保留了概率。进化法必须是完全积极且规范的地图。我们证明，如果动力学是没有内存的，则有两个类别的类别，一个类别具有经典相位空间中有限的跳跃，一个是连续的。我们找到了每类经典量词主方程中最通用的形式。这是通过使用适用于经典Quantum Systems的广义cauchy-Schwartz不平等应用完整的阳性条件来实现的。关键的技术结果是Pawula定理的概括。
Coupling between quantum and classical systems is consistent, provided the evolution is linear in the state space, preserves the split of systems into quantum and classical degrees of freedom, and preserves probabilities. The evolution law must be a completely positive and norm preserving map. We prove that if the dynamics is memoryless, there are two classes of these dynamics, one which features finite sized jumps in the classical phase space and one which is continuous. We find the most general form of each class of classical-quantum master equation. This is achieved by applying the complete positivity conditions using a generalized Cauchy-Schwartz inequality applicable to classical-quantum systems. The key technical result is a generalisation of the Pawula theorem.
