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

TL;DR

This paper presents a quantum electrodynamics-based method to simulate the time evolution of atomic and molecular systems, capturing phenomena like electron-positron oscillations and effects of self-energy on electron mass.

Contribution

It introduces a novel approach using localized wavepackets and equations of motion in QED to model dynamic electronic and virtual particle processes in atoms and molecules.

Findings

Observation of electron-positron oscillations in charge density

Shortening of oscillation period with self-energy effects

Numerical demonstration on hydrogen atom and molecule

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.