Department of Chemistry and Biochemistry, University of South Carolina, Columbia, South Carolina 29208, USA.
J Chem Phys. 2011 Jul 21;135(3):034104. doi: 10.1063/1.3610165.
The Boltzmann evolution of a wavefunction can be recast as imaginary-time dynamics of the quantum trajectory ensemble. The quantum effects arise from the momentum-dependent quantum potential--computed approximately to be practical in high-dimensional systems--influencing the trajectories in addition to the external classical potential [S. Garashchuk, J. Chem. Phys. 132, 014112 (2010)]. For a nodeless wavefunction represented as ψ(x, t) = exp(-S(x, t)/ħ) with the trajectory momenta defined by ∇S(x, t), analysis of the Lagrangian and Eulerian evolution shows that for bound potentials the former is more accurate while the latter is more practical because the Lagrangian quantum trajectories diverge with time. Introduction of stationary and time-dependent components into the wavefunction representation generates new Lagrangian-type dynamics where the trajectory spreading is controlled improving efficiency of the trajectory description. As an illustration, different types of dynamics are used to compute zero-point energy of a strongly anharmonic well and low-lying eigenstates of a high-dimensional coupled harmonic system.
波函数的玻尔兹曼演化可以重新表述为量子轨迹系综的虚时动力学。量子效应来自于除外部经典势之外还会影响轨迹的动量相关量子势——这是通过近似计算在高维系统中实现的[S. Garashchuk, J. Chem. Phys. 132, 014112 (2010)]。对于没有节点的波函数表示为 ψ(x, t) = exp(-S(x, t)/ħ)，其中轨迹动量由 ∇S(x, t) 定义，对拉格朗日和欧拉演化的分析表明，对于束缚势，前者更准确，而后者更实用，因为拉格朗日量子轨迹随着时间的推移而发散。在波函数表示中引入静止和时变分量会产生新的拉格朗日型动力学，其中轨迹扩散受到控制，从而提高轨迹描述的效率。作为说明，不同类型的动力学用于计算强非谐势阱的零点能和高维耦合谐振系统的低能本征态。
