Dynamics of the Aharonov-Bohm effect

TL;DR

This paper investigates the time-dependent behavior of electron wave packets in the Aharonov-Bohm effect using a numerical solution of the Dirac equation, revealing velocity changes in regions without magnetic fields.

Contribution

It introduces a 3D FDTD method to solve the Dirac equation for studying electron dynamics in Aharonov-Bohm setups, providing new insights into quantum-classical correspondence.

Findings

Electron wave packet velocity changes without local magnetic fields.

Qualitative agreement with classical conservation of generalized momentum.

Demonstrates the effectiveness of 3D FDTD in quantum dynamics simulations.

Abstract

The time-dependent Dirac equation is solved using the three-dimensional Finite Difference-Time Domain (FDTD) method. The dynamics of the electron wave packet in a vector potential is studied in the arrangements associated with the Aharonov-Bohm effect. The solution of the Dirac equation showed a change in the velocity of the electron wave packet even in a region where no fields of the unperturbed solenoid acted on the electron. The solution of the Dirac equation qualitatively agreed with the prediction of classical dynamics under the assumption that the dynamics was defined by the conservation of generalized or canonical momentum of the electron.