HeTDSE: A GPU based program to solve the full-dimensional time-dependent Schrödinger equation for two-electron helium subjected to strong laser fields*

Abstract

Electron–electron correlation plays an important role in the underlying dynamics in physics and chemistry. Helium is the simplest and most fundamental two-electron system. The dynamic process of helium in a strong laser field is still a challenging issue because of the large calculation cost. In this study, a graphic processing unit (GPU) openACC based ab initio numerical simulations package HeTDSE is developed to solve the full-dimensional time-dependent Schrödinger equation of helium subjected to a strong laser pulse. HeTDSE uses B-spline basis sets expansion method to construct the radial part of the wavefunction, and the spherical harmonic functions is used to express for the angular part. Adams algorithm is employed for the time propagation. Our example shows that HeTDSE running on an NVIDIA Kepler K20 GPU can outperform the one on an Intel E5-2640 single CPU core by a factor of 147. HeTDSE code package can be obtained from the author or from the author’s personal website (doi: 10.13140/RG.2.2.15334.45128) directly under the GPL license, so HeTDSE can be downloaded, used and modified freely.

Quantum dynamics of positron-hydrogen scattering and three-body bound state formation with an assisting laser field: predictions of a reduced-dimensionality model

“…In full dimensionality, even for the simplest positron-hydrogen system, one generally needs to discretize one time dimension and six space dimensions (three for the positron and the other three for the electron). Performing the time evolution of the system wave function in complete six-dimensional space is still a formidable task, even on today's supercomputers [36][37][38]. In the present work, we adopt a one-dimensional scattering model that has been extensively applied to laserassisted scattering [39][40][41][42][43].…”