Department of Chemistry and Centre for Scientific Computing, University of Warwick, Coventry CV4 7AL, United Kingdom.
J Chem Phys. 2013 Sep 14;139(10):104107. doi: 10.1063/1.4819322.
We introduce a new approach for calculating quantum time-correlation functions and time-dependent expectation values in many-body thermal systems; both electronically adiabatic and non-adiabatic cases can be treated. Our approach uses a path integral simulation to sample an initial thermal density matrix; subsequent evolution of this density matrix is equivalent to solution of the time-dependent Schrödinger equation, which we perform using a linear expansion of Gaussian wavepacket basis functions which evolve according to simple classical-like trajectories. Overall, this methodology represents a formally exact approach for calculating time-dependent quantum properties; by introducing approximations into both the imaginary-time and real-time propagations, this approach can be adapted for complex many-particle systems interacting through arbitrary potentials. We demonstrate this method for the spin Boson model, where we find good agreement with numerically exact calculations. We also discuss future directions of improvement for our approach with a view to improving accuracy and efficiency.
我们介绍了一种新的方法来计算多体热系统中的量子时间相关函数和时变期望；既可以处理电子绝热情况，也可以处理非绝热情况。我们的方法使用路径积分模拟来采样初始热密度矩阵；随后，这个密度矩阵的演化相当于求解含时薛定谔方程，我们使用高斯波包基函数的线性展开来执行这个方程，这些基函数根据简单的类经典轨迹演化。总的来说，这种方法是一种计算时变量子性质的严格方法；通过在虚时和实时传播中引入近似，这种方法可以适应通过任意势相互作用的复杂多粒子系统。我们用自旋玻色子模型来演示这个方法，发现与数值精确计算结果吻合良好。我们还讨论了我们的方法的未来改进方向，以提高准确性和效率。
