What happens to wavepackets of fermions when scattered by the Maldacena-Ludwig wall?

TL;DR

This paper investigates how wavepackets of fermions behave when scattered by a boundary condition that produces exotic, fractionally-charged excitations, revealing localized charge densities and divergent fermion number expectations.

Contribution

It provides an explicit expression for the outgoing state of fermion wavepackets after scattering by the Maldacena-Ludwig boundary, analyzing their charge and particle number properties.

Findings

Charge density is localized with finite, fractional integral.

Expected fermion number diverges for localized wavepackets.

Outgoing state properties depend on wavepacket localization.

Abstract

We study wavepackets of exotic excitations after two-dimensional fermions are scattered by the boundary condition constructed by Maldacena and Ludwig, which turns elementary excitations into exotic fractionally-charged objects. They are of interest in the s-wave approximation of the fermion-monopole scattering in four-dimensional QED and of the multi-channel Kondo effect. We in particular give an explicit expression of the outgoing state of a pair of such particles; we then examine its properties, such as the charge density $\langle J(x)\rangle$ and the expectation value $\langle N\rangle$ of the number of fermions and anti-fermions in the state. The charge density $\langle J(x)\rangle$ is found to be localized with its integral finite and fractional, while the expectation value $\langle N\rangle$ diverges when the wavepacket is localized to a point.