AnalyticQ-ball solutions and their stability in a piecewise parabolic potential

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 spacetime 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. *

Some properties ofU(1)gaugedQ-balls

“…Indeed, in the nongauged case the charge tends to infinity in the limits ω → 0 and ω → M [18]. According to the results of Section 3, the nongauged limit ω → M transforms into the Q-ball with ω = M. This Q-ball corresponds to the lower points with ω M = 1 in Fig.…”

“…From [3] we know that if ω = 0 for a gauged Q-ball, then A 0 ≡ 0. Since there is not a Q-ball solution with the zero charge for ω = 0 in the nongauged case [18], there should be no such solution in the gauged case too. It is also improbable that the charge of a gauged Q-ball tends to infinity in the limit ω → 0 -the value of ω tends to zero, whereas A 0 (r) < 0 is a monotonically growing function such that ω + eA 0 (r) > 0 for any r. Thus, |eA 0 (r)| < ω → 0, whereas a solution for A 0 (r) should support the existence of a large charge.…”

“…(such piecewise potentials for the case of nongauged Q-balls were introduced in [1] and thoroughly examined in [17,18]). Again, it is convenient to pass to the new variables…”

Kink interactions in the(1+1)-dimensionalφ6model

“…On the other hand, the case of (1+1) dimensions can be more easily investigated, hence the use of (1+1)-dimensional systems as simplified models. Note that it is an actively developing area, with many important results obtained recently: the topological defect deformation procedure [4,5], the construction of a topological defect carrying U(1) charge in a system with two scalar fields -one real and one complex [6,7], Q balls in scalar theories with U(1) symmetry [8,9], and many others. There are interesting results in scalar systems with an interaction with a spinor field [10][11][12].…”

Radiative corrections and instability of large Q-balls

“…Moreover, one can consider linear stability of solutions in this model by explicit separation of variables [25]. On the stable branch of solutions E ∼ Q 3/4 and charge could be infinitely large for ω → 0.…”