论文标题
非马克维亚随机Schrödinger方程的Markovian嵌入程序
Markovian Embedding Procedures for Non-Markovian Stochastic Schrödinger Equations
论文作者
论文摘要
我们介绍了非马克维亚随机schrödinger方程的嵌入程序，这是由对量子系统和浴室环境结合的研究引起的。通过引入辅助波函数，可以证明非马克维亚动力学可以嵌入扩展，但马尔可夫，但随机模型。提出了两个嵌入程序。第一种方法导致非线性随机方程，其实现比非马克维亚随机Schrödinger方程更有效。 从第二个过程获得的随机schrödinger方程涉及更多的辅助波函数，但是方程是线性的，我们得出了密度 - 马托里克体的相应的广义量子主方程。通过拟合功率谱来确保嵌入式模型的准确性。使用Ornstein-uhlenbeck过程的线性叠加表示随机力，该过程被掺入辅助schrödinger方程中。通过使用相关随机过程，可以保留低频状态中光谱密度的渐近行为。 通过使用旋转玻色子系统作为测试示例来验证近似值。
We present embedding procedures for the non-Markovian stochastic Schrödinger equations, arising from studies of quantum systems coupled with bath environments. By introducing auxiliary wave functions, it is demonstrated that the non-Markovian dynamics can be embedded in extended, but Markovian, stochastic models. Two embedding procedures are presented. The first method leads to nonlinear stochastic equations, the implementation of which is much more efficient than the non-Markovian stochastic Schrödinger equations. The stochastic Schrödinger equations obtained from the second procedure involve more auxiliary wave functions, but the equations are linear, and we derive the corresponding generalized quantum master equation for the density-matrix. The accuracy of the embedded models is ensured by fitting to the power spectrum. The stochastic force is represented using a linear superposition of Ornstein-Uhlenbeck processes, which are incorporated as multiplicative noise in the auxiliary Schrödinger equations. The asymptotic behavior of the spectral density in the low frequency regime is preserved by using correlated stochastic processes. The approximations are verified by using a spin-boson system as a test example.
