Ballistic dynamics of Dirac particles in electro-magnetic fields

TL;DR

This paper studies the ballistic spreading of states in two-dimensional Dirac operators under electric and magnetic fields, using spectral analysis and Lorentz boosts to derive new bounds.

Contribution

It introduces new Hilbert-Schmidt bounds and applies Lorentz boosts to analyze the spectral dynamics of Dirac particles in electromagnetic fields with symmetry.

Findings

Absolutely continuous states spread ballistically.

New Hilbert-Schmidt bounds are established.

Lorentz boosts are used to derive spectral estimates.

Abstract

Investigating properties of two-dimensional Dirac operators coupled to an electric and a magnetic field (perpendicular to the plane) requires in general unbounded (vector-) potentials. If the system has a certain symmetry, the fields can be described by one-dimensional potentials $V$ and $A$. Assuming that $|A|<|V|$ outside some arbitrary large ball, we show that absolutely continuous states of the effective Dirac operators spread ballistically. These results are based on well-known methods in spectral dynamics together with certain new Hilbert-Schmidt bounds. We use Lorentz boosts to derive these new estimates.