论文标题
海森伯格的开放量子系统图片
Heisenberg Picture for Open Quantum Systems
论文作者
论文摘要
在本说明中，我们开发了一个框架，以描述海森伯格图片中的开放量子系统，即通过时间不断发展的操作员代数。我们指出了这方面的先前提案的不完整性。我们认为，开放量子系统的完整海森堡图片涉及可观察到的每个系统的多个图像海森堡操作员。对于可观察到的给定系统，此类图像运算符的数量等于Hilbert空间环境的尺寸。我们在系统环境耦合中的扰动表达中，根据单个一个点运算符，准确至系统环境中的任意顺序。该表达非线性取决于环境状态。这种扰动表达可以等效地认为是在开放量子系统的希尔伯特空间上变形了算子。在马尔可夫限制中，一个点运算符通过伴随的lindblad方程演变。我们使用简单的自旋系统说明了这些想法。
In this note, we develop a framework to describe open quantum systems in the Heisenberg picture, i.e., via time evolving operator algebras. We point out the incompleteness of the previous proposals in this regard. We argue that a complete Heisenberg picture for an open quantum system involves multiple image Heisenberg operators for each system observable. For a given system observable, the number of such image operators is equal to the dimension of the environment Hilbert space. We derive a perturbative expression, accurate upto arbitrary orders in the system environment coupling, for these image operators in terms of a single one point operator. This expression depends non-linearly on the state of the environment. This perturbative expression can equivalently be thought of as deforming the operator product on the Hilbert space of the open quantum system. In the Markovian limit, the one point operator evolves by an adjoint Lindblad equation. We illustrate these ideas using a simple spin system.
