Moving boundary truncated grid method: Multidimensional quantum dynamics

Abstract

The moving boundary truncated grid (TG) method is used to study wave packet dynamics of multidimensional quantum systems. As time evolves, appropriate Eulerian grid points required for propagating a wave packet are activated and deactivated with no advance information about the dynamics. This method is applied to the Henon-Heiles potential and wave packet barrier scattering in two, three, and four dimensions. Computational results demonstrate that the TG method not only leads to a great reduction in the number of grid points needed to perform accurate calculations but also is computationally more efficient than the full grid calculations.adaptive grid, Henon-Heiles potential, moving boundary truncated grid method, quantum barrier scattering, wave packet dynamics

Moving Boundary Truncated Grid Method: Application to the Time Evolution of Distribution Functions in Phase Space

“…Computational Details. As shown in our previous work, 93 having a high-performance code is the key to overcome the computational overhead and achieve speed acceleration in moving boundary TG calculations. Our implementation of the method 110 is based on a sharedmemory scheme with loop-level OpenMP parallelism.…”

“…Although decreasing the values of the TG parameters leads to an increase in the total number of the TG points, computational results demonstrated that the computational cost for the TG method still greatly decreases with the dimensionality of the system. 93 Furthermore, as discussed in Section 2.2.4, a switch function can be implemented in the computer program that toggles between the FG and TG modes to ensure the efficiency and accuracy of our TG calculation.…”

“…The TG method has been used to integrate the TDSE for wave packet dynamics in two, three, and four dimensions in our previous study. 93 Thus, this method can be readily applied to the atom-diatomic reactive scattering problems. 71 Work is underway to extend the methodology to the coupled TDSEs for electronic nonadiabatic dynamics.…”

“…In our previous studies, , the moving boundary TG method was developed to integrate the TDSE and the ITSE for multidimensional quantum systems. This method can be readily extended to the time evolution of the distribution functions in phase space.…”

“…87−89 Ensembles of correlated trajectories have been employed to propagate the complexvalued density matrix in the Caldeira−Leggett equation. 90,91 The purpose of the present study is to extend the moving boundary truncated grid (TG) method, developed in our previous studies for integration of the TDSE and the imaginary time Schrodinger equation (ITSE), 92,93 to the time evolution of distribution functions in phase space. In the TG method, a variable number of phase space grid points in the Eulerian representation are used to integrate the equation of motion for the distribution function, and the boundaries of the TG are adaptively determined as the distribution function evolves in time.…”