Linearized Q-Ball Perturbations

TL;DR

This paper analyzes linearized perturbations of low-amplitude Q-balls, decomposing them into relativistic, Floquet, and Feshbach-type modes, with explicit forms provided for most modes at leading order.

Contribution

It provides a comprehensive closed-form analysis of perturbation modes of Q-balls, including relativistic and Floquet modes, expanding understanding of their stability and dynamics.

Findings

Modes oscillate at mirror frequencies averaging to the Q-ball frequency.

Corotating modes include breathers and loosely bound states.

Counterrotating modes involve a P"oschl-Teller potential with Feshbach-type quasinormal modes.

Abstract

Linearized deformations of the thick-walled (low-amplitude) (1+1)-dimensional Q-ball may be decomposed into relativistic modes, which are roughly plane waves, and also long-wavelength corotating and counterrotating Floquet modes. Each mode oscillates at a pair of mirror frequencies which average to the Q-ball frequency. The corotating modes are those of a breather or oscillon plus a very loosely bound mode. The counterrotating modes are described by an irrational-level P\"oschl-Teller potential, with two discrete modes which mix with their unbound mirrors, unbinding them and turning them into Feshbach-type quasinormal modes. Expanding to leading order in the Q-ball amplitude, we present all of these modes in closed form, except for the bound mode which does not exist at leading order.