论文标题
开放量子系统的大胆细微示意蒙特卡洛法
The Bold-Thin-Bold Diagrammatic Monte Carlo Method for Open Quantum Systems
论文作者
论文摘要
我们提供了两种图形蒙特卡洛方法，用于量子系统，并加上谐波浴，它们的动力学是通过截然不同的方程式描述的。第一种方法可以被视为戴森系列的重新印象，第二种方法称为“大胆的图形蒙特卡洛”，是基于戴森系列中图表的重新召集以加速其收敛性。与两种方法相关的管理方程的基本机制在于路径积分的复发关系，这是数值方法中最昂贵的部分。所提出的算法给出了工作的扩展[“量子系统浴动力学中的浴缸计算的快速算法”，即将出现的计算机物理通信的模拟”，其中算法的设计基于以前的浴缸影响功能的重用。与其中的算法相比，我们的方法进一步包括重复使用系统相关功能，并在计算效率和内存成本方面表现出更好的性能。我们在自旋 - 玻色子模型的框架中演示了两种方法，并进行了数值实验以验证该方法的有效性。
We present two diagrammatic Monte Carlo methods for quantum systems coupled with harmonic baths, whose dynamics are described by integro-differential equations. The first approach can be considered as a reformulation of Dyson series, and the second one, called "bold-thin-bold diagrammatic Monte Carlo", is based on resummation of the diagrams in the Dyson series to accelerate its convergence. The underlying mechanism of the governing equations associated with the two methods lies in the recurrence relation of the path integrals, which is the most costly part in the numerical methods. The proposed algorithms give an extension to the work ["Fast algorithms of bath calculations in simulations of quantum system-bath dynamics", Computer Physics Communications, to appear], where the algorithms are designed based on reusing the previous calculations of bath influence functionals. Compared with the algorithms therein, our methods further include the reuse of system associated functionals and show better performance in terms of computational efficiency and memory cost. We demonstrate the two methods in the framework of spin-boson model, and numerical experiments are carried out to verify the validity of the methods.
