Hughes Keith H, Parry Steven M, Burghardt Irene
School of Chemistry, Bangor University, Bangor, Gwynedd LL57 2UW, United Kingdom.
J Chem Phys. 2009 Feb 7;130(5):054115. doi: 10.1063/1.3073759.
The hydrodynamic formulation of mixed quantum states involves a hierarchy of coupled equations of motion for the momentum moments of the Wigner function. In this work a closure scheme for the hierarchy is developed. The closure scheme uses information contained in the lower known moments to expand the Wigner phase-space distribution function in a Gauss-Hermite orthonormal basis. The higher moment required to terminate the hierarchy is then easily obtained from the reconstructed approximate Wigner function by a straightforward integration over the momentum space. Application of the moment closure scheme is demonstrated for the dissipative and nondissipative dynamics of two different systems: (i) double-well potential, (ii) periodic potential.
混合量子态的流体动力学公式涉及维格纳函数动量矩的耦合运动方程层次结构。在这项工作中，开发了一种针对该层次结构的封闭方案。该封闭方案利用较低已知矩中包含的信息，在高斯-厄米特正交基中展开维格纳相空间分布函数。然后，通过在动量空间上的直接积分，从重构的近似维格纳函数中轻松获得终止层次结构所需的更高矩。针对两个不同系统的耗散和非耗散动力学演示了矩封闭方案的应用：（i）双阱势，（ii）周期势。
