论文标题
在半古典路径积分表达式中涉及未来的非马克维亚轨迹
Non-Markovian trajectories involving future in the semi-classical path integral expression
论文作者
论文摘要
基于固定相条件得出的量子系统的半经典路径积分表达是耦合到谐波浴的。发现系统路径是非马克维亚人的。最引人注目的是，系统路径不仅与它的过去（如Langevin方程中）相结合，而且还伴随着它的未来，即系统的运动方程是始终涉及的整体差异方程。进行数值测试以确认确实需要未来的涉及项。由于方程式的未来 - 马多维亚性质，无法通过迭代方法获得数值解。相反，必须采用根搜索算法。
Semiclassical path integral expression for a quantum system coupled to a harmonic bath is derived based on the stationary phase condition. It is discovered that the system path is non-Markovian. Most strikingly, the system path not only couples to its past (as in the Langevin equation), but also to its future, i.e. the equation of motion for the system is an integro-differential equation that involves all times. Numerical tests are performed to confirm that the future-involved term is indeed necessary. Because of the future-non-Markovian nature of the equation, the numerical solution cannot be obtained by iterative methods. Instead, root search algorithms must be employed.
