论文标题
打开量子系统和Lindblad方程的现场理论方法
Field-theoretical approach to open quantum systems and the Lindblad equation
论文作者
论文摘要
我们开发了一种系统的现场理论方法，以基于凝结的多体方法打开量子系统。开放量子系统还原密度矩阵的时间演变由传输矩阵确定。开发图形扰动理论，援引Wick的定理与热平衡中的Caldeira-Leggett量子振荡器环境有关，传输矩阵满足了以不可修复内核为特征的Dyson方程。与Nakajima-Zwanzig和标准方法不同，Dyson方程相当于降低的密度矩阵的一般非马克维亚主方程，具有世俗效应，并且与初始制剂无关。内核取决于相互作用幂的系统图形扩展。我们认为内核的天生近似值。应用凝结的杆或等效地，等效于通常假设时间尺度分离，我们得出了Markov类型的主方程。此外，施加了旋转波近似，我们获得了Lindblad形式的Markov主方程。为了说明该方法，我们考虑了与热热浴的单个值的标准示例。
We develop a systematic field-theoretical approach to open quantum systems based on condensed-matter many-body methods. The time evolution of the reduced density matrix for the open quantum system is determined by a transmission matrix. Developing diagrammatic perturbation theory, invoking Wick's theorem in connection with a Caldeira-Leggett quantum oscillator environment in thermal equilibrium, the transmission matrix satisfies a Dyson equation characterized by an irreducible kernel. Unlike the Nakajima-Zwanzig and standard approaches, the Dyson equation is equivalent to a general non-Markovian master equation for the reduced density matrix, incorporating secular effects and independent of the initial preparation. The kernel is determined by a systematic diagrammatic expansion in powers of the interaction. We consider the Born approximation for the kernel. Applying a condensed-matter pole or, equivalently, a quasiparticle-type approximation, equivalent to the usual assumption of a timescale separation, we derive a master equation of the Markov type. Furthermore, imposing the rotating-wave approximation,we obtain a Markov master equation of the Lindblad form. To illustrate the method, we consider the standard example of a single qubit coupled to a thermal heat bath.
