混合量子-经典Liouville方程的正-反轨线解分析
Analysis of the Forward-Backward Trajectory Solution for the Mixed Quantum-Classical Liouville Equation
摘要：
混合量子-经典方法为模拟大型复杂系统中的量子过程提供了强有力的算法。在映射基中的混合量子经典Liouville方程的前向-后向轨道解[J. Chem. Phys. 137，22 A507（2012）]就是这样一种方案。它通过量子相干态变量的向前和向后轨迹的传播以及由向前和向后轨迹共同确定的平均场势上的浴轨迹的传播来模拟动力学。本文分析了该解的性质，给出了其有效性的数值试验和非线性量子过程研究中的实用性研究。此外，我们提出了一个扩展的近似解决方案，允许系统地改善结果。这种扩展，称为跳跃的向前向后的轨迹的解决方案，进行了详细的分析和测试，并讨论了其各种实现。
英文摘要：
Mixed quantum-classical methods provide powerful algorithms for the simulation of quantum processes in large and complex systems. The forward-backward trajectory solution of the mixed quantum-classical Liouville equation in the mapping basis [J. Chem. Phys. 137, 22A507 (2012)] is one such scheme. It simulates the dynamics via the propagation of forward and backward trajectories of quantum coherent state variables, and the propagation of bath trajectories on a mean-field potential determined jointly by the forward and backward trajectories. An analysis of the properties of this solution, numerical tests of its validity and an investigation of its utility for the study of nonadiabtic quantum processes are given. In addition, we present an extension of this approximate solution that allows one to systematically improve the results. This extension, termed the jump forward-backward trajectory solution, is analyzed and tested in detail and its various implementations are discussed.
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