Adiabatic invariance of oscillons/I-balls

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 a 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 quasistable, 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.