论文标题
开放量子系统的通用Lindblad方程
Universal Lindblad equation for open quantum systems
论文作者
论文摘要
我们以Lindblad形式开发了Markovian主方程，该方程式能够有效研究各种开放量子多体系统，这些系统与现有方法无法访问。主方程的有效性完全基于浴室的属性和系统浴耦合，而没有对系统本身级别结构的任何要求。使用Markov近似与早期方法中使用的Markov近似来得出主程。我们为Markov近似引起的误差提供了严格的结合；误差由浴室的内在相关和松弛时间尺度的无量纲组合控制。我们的主方程在与Bloch-Redfield方程相同的近似级别上是准确的。与Bloch-Redfield方法相反，我们的方法确保了保持密度矩阵的阳性。结果，我们的方法是鲁棒的，可以使用纯态（而不是密度矩阵）的随机演变有效地求解。我们讨论了如何将方法应用于静态或驱动的量子多体系统，并通过对旋转链的数值模拟来说明其功能，该旋转链通过现有方法对治疗可能具有挑战性。
We develop a Markovian master equation in the Lindblad form that enables the efficient study of a wide range of open quantum many-body systems that would be inaccessible with existing methods. The validity of the master equation is based entirely on properties of the bath and the system-bath coupling, without any requirements on the level structure within the system itself. The master equation is derived using a Markov approximation that is distinct from that used in earlier approaches. We provide a rigorous bound for the error induced by this Markov approximation; the error is controlled by a dimensionless combination of intrinsic correlation and relaxation timescales of the bath. Our master equation is accurate on the same level of approximation as the Bloch-Redfield equation. In contrast to the Bloch-Redfield approach, our approach ensures preservation of the positivity of the density matrix. As a result, our method is robust, and can be solved efficiently using stochastic evolution of pure states (rather than density matrices). We discuss how our method can be applied to static or driven quantum many-body systems, and illustrate its power through numerical simulation of a spin chain that would be challenging to treat by existing methods.
