Landau Levels of Scalar QED in Time-Dependent Magnetic Fields

TL;DR

This paper analytically studies the behavior of Landau levels in scalar QED under time-varying magnetic fields, classifying quantum motions and calculating pair-production rates during sudden magnetic field changes.

Contribution

It introduces a formalism to analyze scalar QED Landau levels in time-dependent magnetic fields and derives exact solutions for pair production during abrupt field changes.

Findings

Classifies quantum motions into adiabatic, nonadiabatic, and sudden changes.

Provides exact quantum solutions for Landau levels under dynamic magnetic fields.

Calculates pair-production rate during sudden magnetic field changes.

Abstract

The Landau levels of scalar QED undergo continuous transitions under a homogeneous, time-dependent magnetic field. We analytically formulate the Klein-Gordon equation for a charged spinless scalar as a Cauchy initial value problem in the two-component first order formalism and then put forth a measure that classifies the quantum motions into the adiabatic change, the nonadiabatic change, and the sudden change. We find the exact quantum motion and calculate the pair-production rate when the magnetic field suddenly changes as a step function.