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A New Trajectory Branching Approximation To Propagate the Mixed Quantum-Classical Liouville Equation

机译:传播混合量子经典Liouville方程的新的轨迹分支近似

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Starting from the mixed quantum-classical Liouville (MQCL) equation, we derive a new trajectory branching method as a modification to the conventional mean field approximation. In the new method, the mean field approximation is used to propagate the mixed quantum-classical dynamics for short times. When the mean field description becomes invalid, new trajectories are added in the simulation by branching the single trajectory into multiple ones. To achieve this, a new set of variables are defined to monitor the deviations of the dynamics on different potential energy surfaces from the reference mean field trajectory, and their equations of motion are derived from the MQCL equation based on the method of first moment expansion. The new method is tested on several one-dimensional two surface problems and is shown to correctly solve the problem of the mean field approximation in several cases.
机译:从混合量子经典Liouville(MQCL)方程开始,我们推导了一种新的轨迹分支方法,作为对传统平均场近似的一种改进。在新方法中,均值场近似用于在短时间内传播混合的量子经典动力学。当平均场描述变为无效时,通过将单个轨迹分成多个轨迹,在仿真中添加新轨迹。为此,定义了一组新变量以监视不同势能表面上的动力学与参考平均场轨迹的偏差,并且基于一阶矩展开法从MQCL方程派生了它们的运动方程。该新方法在几个一维两维表面问题上进行了测试,结果证明可以正确解决几种情况下的平均场近似问题。

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