论文标题
戴森方程方法，用于平均马尔可夫流程多个实现的经典和量子可观察物
A Dyson equation approach for averaging of classical and quantum observables on multiple realizations of Markov processes
论文作者
论文摘要
实验技术中的时间依赖性信号，例如核磁共振（NMR）和MUON自旋松弛（MUSR）通常是许多显微镜动力学过程中合奏平均值的结果。尽管有许多用于符合这些信号的功能，但它们通常仅在特定方案中有效，并且几乎永远不会正确描述“光谱扩散”制度，其中动力学以时间尺度与系统的特征频率相当。对这些问题的全面处理将需要一个人在所有可能的依赖性汉密尔顿人的动力学的可能实现上进行一条组成部分。 在本文中，我们提出了一种数值方法，该方法可能有可能用于解决此类时间演变问题，并根据对同一问题的蒙特卡洛模拟进行基准测试。该方法可用于任何类型的动力学，但对于可以近似为Markov过程的任何动力学特别强大，其中每个步骤的动态仅取决于系统的先前状态。该方法用于平均经典和量子可观察物。在后一种情况下，使用了使用liouvillians和密度矩阵的形式主义。
Time dependent signals in experimental techniques such as Nuclear Magnetic Resonance (NMR) and Muon Spin Relaxation (muSR) are often the result of an ensemble average over many microscopical dynamical processes. While there are a number of functions used to fit these signals, they are often valid only in specific regimes, and almost never properly describe the "spectral diffusion" regime, in which the dynamics happen on time scales comparable to the characteristic frequencies of the system. Full treatment of these problems would require one to carry out a path integral over all possible realizations of the dynamics of the time dependent Hamiltonian. In this paper we present a numerical approach that can potentially be used to solve such time evolution problems, and we benchmark it against a Monte Carlo simulations of the same problems. The approach can be used for any sort of dynamics, but is especially powerful for any dynamics that can be approximated as Markov processes, in which the dynamics at each step only depend on the previous state of the system. The approach is used to average both classical and quantum observables; in the latter case, a formalism making use of Liouvillians and density matrices is used.
