arXiv 1408.37582014-08quant-ph

开放量子动力学中的对称性

Symmetries in open quantum dynamics

Thomas F. Jordan

备注：: 28 pages, presentation improved

摘要：

简单的例子是用来介绍和检查对称性的开放量子动力学，可以描述的幺正算子。对于整个封闭系统的哈密尔顿动力学，对称性采取预期的形式，当哈密尔顿算子有一个下界时，表示酉对称算子与哈密尔顿算子交换。还有更多的对称性只适用于子系统的开放动力学。例子表明，这些对称性如何单独可以揭示动力学的属性，并减少需要做什么工作的动力学。一个子系统的开放动力学的对称性甚至可以暗示整个系统的动力学的性质，而不是整个系统的动力学的对称性所暗示的。对于子系统的开放动力学，对称性通常与运动常数无关。有许多对称性在薛定谔图像中不能被看作是子系统的密度矩阵的动力学映射的对称性。有一个子系统的开放动力学的对称性，只依赖于动力学。在最简单的例子中，这些也是整个系统动力学的对称性。还有更多的对称性，一种新的对称性，也取决于子系统和整个系统的其余部分之间的相关性或不相关性，或者取决于整个系统其余部分的状态。

英文摘要：

Simple examples are used to introduce and examine symmetries of open quantum dynamics that can be described by unitary operators. For the Hamiltonian dynamics of an entire closed system, the symmetry takes the expected form which, when the Hamiltonian has a lower bound, says that the unitary symmetry operator commutes with the Hamiltonian operator. There are many more symmetries that are only for the open dynamics of a subsystem. Examples show how these symmetries alone can reveal properties of the dynamics and reduce what needs to be done to work out the dynamics. A symmetry of the open dynamics of a subsystem can even imply properties of the dynamics for the entire system that are not implied by the symmetries of the dynamics of the entire system. The symmetries are generally not related to constants of the motion for the open dynamics of the subsystem. There are many symmetries that cannot be seen in the Schrodinger picture as symmetries of dynamical maps of density matrices for the subsystem. There are symmetries of the open dynamics of a subsystem that depend only on the dynamics. In the simplest examples, these are also symmetries of the dynamics of the entire system. There are many more symmetries, of a new kind, that also depend on correlations, or absence of correlations, between the subsystem and the rest of the entire system, or on the state of the rest of the entire system.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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