Compact Q-balls and Q-shells in a scalar electrodynamics

TL;DR

This paper explores spherically symmetric non-topological solitons called Q-balls and Q-shells in scalar electrodynamics with a specific self-interaction potential, revealing their properties and energy-charge relationships.

Contribution

It demonstrates the existence of Q-balls and Q-shells with compact support in scalar electrodynamics using a signum-Gordon type potential, detailing their energy dependence on charge.

Findings

Q-balls occur at small charge values with E ~ |Q|^(5/6)

Q-shells occur at large charge values with E ~ |Q|^(7/6)

Charge density vanishes outside a compact region in space

Abstract

We investigate spherically symmetric non topological solitons in electrodynamics with a scalar field self interaction U ~|\psi| taken from the complex signum-Gordon model. We find Q-balls for small absolute values of the total electric charge Q, and Q-shells when |Q| is large enough. In both cases the charge density exactly vanishes outside certain compact region in the three dimensional space. The dependence of the total energy E of small Q-balls on the total electric charge has the form E ~ |Q|^(5/6), while in the case of very large Q-shells E ~ |Q|^(7/6).