Method of first-principles numerical simulation for time-evolving electronic states

Akira Endoh, Shigehiko Sasa, Hiroshi Arimoto +1 more

We performed time-evolved numerical simulation of a two-dimensional electron wave packet through a double slit by solving the time-dependent Schrödinger equation using the finite difference method to simulate the electron interference phenomenon of a single electron. The propagating directions of interference peaks show that the starting point of electron interference is the center between the two slit exits. The number of interference peaks and their angles are found to be independent of potential barrier thickness. These results are compared with the results of our previous calculation of electron diffraction through a single slit.

Qing Peng

Piotr Deuar, P. D. Drummond

First principles simulations of the quantum dynamics of interacting Bose gases using the stochastic gauge representation are analysed. In a companion paper, we showed how the positive-P representation can be applied to these problems using stochastic differential equations. That method, however, is limited by increased sampling error as time evolves. Here, we show how the sampling error can be greatly reduced and the simulation time significantly extended using stochastic gauges. In particular, local stochastic gauges (a subset) are investigated. Improvements are confirmed in numerical calculations of single-, double- and multi-mode systems in the weak-mode coupling regime. Convergence issues are investigated, including the recognition of two modes by which stochastic equations produced by phase-space methods in general can diverge: movable singularities and a noise-weight relationship. The example calculated here displays wave-like behaviour in spatial correlation functions propagating in a uniform 1D gas after a sudden change in the coupling constant. This could in principle be tested experimentally using Feshbach resonance methods.

Xiao Zheng

Akira Endoh, Shigehiko Sasa, Shunichi Muto

We performed time-evolved numerical simulation of a two-dimensional electron wave packet through a quantum point contact using the finite difference method to simulate the diffraction phenomenon of a single electron. We found that the transmitted wave packet has diffracted subpeaks which show the following properties: (1) The traces of diffracted subpeaks start from the center of the slit entrance. (2) Lateral wave number of diffracted subpeaks is quantized. (3) The diffraction angles are determined by slit width and the initial electron wave packet energy. (4) The number of allowed diffracted subpeaks is determined by potential barrier thickness. (5) There is a delay in the motion of diffracted subpeaks due to quantization inside the slit.

Robert L. Sugar