论文标题
预测开放系统非线性光谱的有效数值方法
Efficient numerical method for predicting nonlinear optical spectroscopies of open systems
论文作者
论文摘要
非线性光谱镜是用于探测分子和纳米级系统中量子动力学的强大工具。尽管有关超快光谱镜的直觉通常是通过考虑脉冲脉冲来构建的，但实际的实验具有有限的持续性脉冲，这对于解释和预测实验结果可能很重要。我们提出了一种新的用于光谱建模的新型开源方法，称为超快超快（UF $^2 $）光谱，该方法可实现非线性光谱的计算有效且方便的预测，包括对任意有限持续时间的脉冲脉冲形状的处理。 uf $^2 $是一种基于傅立叶的方法，需要对系统密度矩阵的Liouvillian繁殖物进行对角化。我们还提出了runge-kutta euler（RKE）直接传播方法。我们包括带有马尔可夫浴室的世俗红菲尔德，全雷德菲尔德和lindblad形式主义的开放系统动态。对于非马克维亚系统，将与记忆效应相对应的自由度带入了系统中并进行非扰动处理。我们分析算法的计算复杂性，并以数值证明，包括对角度化传播器的成本，UF $^2 $比直接传播方法的速度比具有任意希尔伯特空间维度的直接传播方法快20-200倍；对于全红场模型来说，它的速度也更快，至少直到传播器需要超过20 GB才能存储的系统尺寸；对于Lindblad型号而言，它的速度更快到100附近的尺寸，对小型系统的加速度超过500。uf $^2 $和RKE是较大的开源Ultrafast Software Suite的一部分，其中包括用于自动生成和计算Feynman图的工具。
Nonlinear optical spectroscopies are powerful tools for probing quantum dynamics in molecular and nanoscale systems. While intuition about ultrafast spectroscopies is often built by considering impulsive optical pulses, actual experiments have finite-duration pulses, which can be important for interpreting and predicting experimental results. We present a new freely available open source method for spectroscopic modeling, called Ultrafast Ultrafast (UF$^2$) Spectroscopy, which enables computationally efficient and convenient prediction of nonlinear spectra, including treatment of arbitrary finite duration pulse shapes. UF$^2$ is a Fourier-based method that requires diagonalization of the Liouvillian propagator of the system density matrix. We also present a Runge-Kutta Euler (RKE) direct propagation method. We include open-systems dynamics in the secular Redfield, full Redfield, and Lindblad formalisms with Markovian baths. For non-Markovian systems, the degrees of freedom corresponding to memory effects are brought into the system and treated nonperturbatively. We analyze the computational complexity of the algorithms and demonstrate numerically that, including the cost of diagonalizing the propagator, UF$^2$ is 20-200 times faster than the direct propagation method for secular Redfield models with arbitrary Hilbert space dimension; that it is similarly faster for full Redfield models at least up to system dimensions where the propagator requires more than 20 GB to store; and that for Lindblad models it is faster up to dimension near 100, with speedups for small systems by factors of over 500. UF$^2$ and RKE are part of a larger open source Ultrafast Software Suite, which includes tools for automatic generation and calculation of Feynman diagrams.
