Does the oscillatory behavior of the Momentum Spectrum depend on the basis in the Post-Transient Stage?

TL;DR

This paper investigates how the oscillatory behavior of the momentum spectrum of particle pairs created by a time-dependent electric field varies with the choice of adiabatic basis, revealing a novel dynamical scaling property.

Contribution

It demonstrates that the oscillatory momentum spectra depend on the basis but can be aligned through a specific time scaling related to the transient stage.

Findings

Oscillatory spectra depend on the adiabatic basis used.

A dynamical scaling aligns spectra from different bases.

Multi-modal spectra appear in the multi-photon regime at finite times.

Abstract

Pair creation by a spatially homogeneous, time-dependent electric field is studied within the framework of scalar quantum electrodynamics. We employ the standard Bogoliubov transformation approach to compute the single-particle distribution function in an adiabatic basis. We analyzed the distribution function of created particles in two different adiabatic bases (related by a unitary transformation). A novel dynamical scaling is observed while analyzing the oscillatory momentum spectrum of the pairs created by the Sauter pulsed field at intermediate times, calculated using the two adiabatic bases. In these bases, the same oscillatory momentum spectra are observed but at different times. However, when we scale the time by the point marking the end of the transient stage of dynamical evolution for each case of central momentum, the respective momentum spectra overlap. Furthermore, we study the time evolution of the momentum spectrum in the multi-photon regime and find that the spectra show a multi-modal profile structure at finite times for both choices of basis.