Analytic Q-ball solutions and their stability in a piecewise parabolic potential

TL;DR

This paper analytically derives and examines the stability of Q-ball solutions in a complex scalar field model with a piecewise parabolic potential across different dimensions, identifying conditions for stability and instability.

Contribution

It provides explicit analytical solutions for Q-balls in a piecewise parabolic potential and thoroughly analyzes their stability in (1+1) and (3+1) dimensions.

Findings

Existence of both stable and unstable Q-ball solutions depending on parameters.

Explicit linear stability analysis showing exponential growth modes for some solutions.

Identification of parameter regimes for classical stability in (1+1)-dimensional space.

Abstract

Explicit solutions for extended objects of a Q-ball type were found analytically in a model describing complex scalar field with piecewise parabolic potential in (3+1)- and (1+1)-dimensional space-times. Such a potential provides a variety of solutions which were thoroughly examined. It was shown that, depending on the values of the parameters of the model and according to the known stability criteria, there exist stable and unstable solutions. The classical stability of solutions in (1+1)-dimensional space-time was examined in the linear approximation and it was shown explicitly that the spectrum of linear perturbations around some solutions contains exponentially growing modes while it is not so for other solutions.