States of the Dirac equation in confining potentials

TL;DR

This paper investigates the Dirac equation in confining potentials, revealing metastable states with increasing lifetimes near the non-relativistic limit, and explores their implications for high energy physics and graphene systems.

Contribution

It demonstrates the existence of metastable states in the Dirac equation with confining potentials and connects their properties to phenomena like pair production and resonant scattering.

Findings

Metastable states have longer lifetimes approaching the non-relativistic limit.

Density of states is well described by Breit-Wigner lines.

Line width reproduces Schwinger pair production rate.

Abstract

We study the Dirac equation in confining potentials with pure vector coupling, proving the existence of metastable states with longer and longer lifetimes as the non-relativistic limit is approached and eventually merging with continuity into the Schr\"odinger bound states. We believe that the existence of these states could be relevant in high energy model construction and in understanding possible resonant scattering effects in systems like Graphene. We present numerical results for the linear and the harmonic cases and we show that the the density of the states of the continuous spectrum is well described by a sum of Breit-Wigner lines. The width of the line with lowest positive energy, as expected, reproduces very well the Schwinger pair production rate for a linear potential: we thus suggest a different way of obtaining informations on the pair production in unbounded, non uniform electric fields, where very little is known.