Adiabatic Invariance of Oscillons/I-balls

TL;DR

This paper proves the adiabatic invariance of oscillons and I-balls in scalar fields with specific potentials, explaining their stability and longevity through numerical verification of conserved adiabatic charge.

Contribution

It demonstrates the adiabatic invariance of oscillons/I-balls for a uniquely determined potential, establishing the link between potential form and stability.

Findings

Adiabatic invariance holds for quadratic potentials with logarithmic corrections.

Oscillons/I-balls are absolutely stable under the specific potential.

Longevity is due to approximate conservation of adiabatic charge.

Abstract

Real scalar fields are known to fragment into spatially localized and long-lived solitons called oscillons or $I$-balls. We prove the adiabatic invariance of the oscillons/$I$-balls for a potential that allows periodic motion even in the presence of non-negligible spatial gradient energy. We show that such potential is uniquely determined to be the quadratic one with a logarithmic correction, for which the oscillons/$I$-balls are absolutely stable. For slightly different forms of the scalar potential dominated by the quadratic one, the oscillons/$I$-balls are only quasi-stable, because the adiabatic charge is only approximately conserved. We check the conservation of the adiabatic charge of the $I$-balls in numerical simulation by slowly varying the coefficient of logarithmic corrections. This unambiguously shows that the longevity of oscillons/$I$-balls is due to the adiabatic invariance.