How parametric resonance mechanism follows quench mechanism in disoriented chiral condensate

Abstract

We show how parametric resonance mechanism follows quench mechanism in the classical linear sigma model. The parametric resonance amplifies long wavelength modes of the pion for more than $10 fm/c$. The shifting from the quench mechanism to the parametric resonance mechanism is described by a time dependent quantity. After the quench mechanism is over, that quantity has an oscillating part, which causes the parametric resonance. Since its frequency is $2 m_\pi ~(m_\pi$ : pion mass), very long wavelength modes such as k = 40 MeV of the pion are amplified by the parametric resonance.