Study of Simulation Method of Time Evolution of Atomic and Molecular Systems by Quantum Electrodynamics

Abstract

We discuss a method to follow step-by-step time evolution of atomic and molecular systems based on QED (Quantum Electrodynamics). Our strategy includes expanding the electron field operator by localized wavepackets to define creation and annihilation operators and following the time evolution using the equations of motion of the field operator in the Heisenberg picture. We first derive a time evolution equation for the excitation operator, the product of two creation or annihilation operators, which is necessary for constructing operators of physical quantities such as the electronic charge density operator. We then describe our approximation methods to obtain time differential equations of the electronic density matrix, which is defined as the expectation value of the excitation operator. By solving the equations numerically, we show "electron-positron oscillations", the fluctuations originated from virtual electron-positron pair creations and annihilations, appear in the charge density of a hydrogen atom and molecule. We also show that the period of the electron-positron oscillations becomes shorter by including the self-energy process, in which the electron emits a photon and then absorbs it again, and it can be interpreted as the increase in the electron mass due to the self-energy.