Quantum parametric resonance

The quantum mechanical equivalent of parametric resonance is studied. A simple model of a periodically kicked harmonic oscillator is introduced which can be solved exactly. Classically stable and unstable regions in parameter space are shown to correspond to Floquet operators with qualitatively different properties. Their eigenfunctions, which are calculated exactly, exhibit a transition: for parameter values with classically stable solutions the eigenstates are normalizable while they cannot be normalized for parameter values with classically unstable solutions. Similarly, the spectrum of quasi energies undergoes a specific transition. These observations remain valid qualitatively for arbitrary linear systems exhibiting classically parametric resonance such as the paradigm example of a frequency modulated pendulum described by Mathieu's equation

How parametric resonance mechanism follows quench mechanism in disoriented chiral condensate

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.Comment: LaTeX, 10 page

Excitation of a Kaluza-Klein mode by parametric resonance

In this paper we investigate a parametric resonance phenomenon of a Kaluza-Klein mode in a $D$-dimensional generalized Kaluza-Klein theory. As the origin of the parametric resonance we consider a small oscillation of a scale of the compactification around a today's value of it. To make our arguments definite and for simplicity we consider two classes of models of the compactification: those by $S_{d}$ ($d=D-4$) and those by $S_{d_{1}}\times S_{d_{2}}$ ($d_1\ge d_2$, $d_{1}+d_{2}=D-4$). For these models we show that parametric resonance can occur for the Kaluza-Klein mode. After that, we give formulas of a creation rate and a number of created quanta of the Kaluza-Klein mode due to the parametric resonance, taking into account the first and the second resonance band. By using the formulas we calculate those quantities for each model of the compactification. Finally we give conditions for the parametric resonance to be efficient and discuss cosmological implications.Comment: 36 pages, Latex file, Accepted for publication in Physical Review

Parametric Resonance For Complex Fields

Recently, there have been studies of parametric resonance decay of oscillating real homogeneous cosmological scalar fields, in both the narrow-band and broad-band case, primarily within the context of inflaton decay and (p)reheating. However, many realistic models of particle cosmology, such as supersymmetric ones, inherently involve complex scalar fields. In the oscillations of complex scalars, a relative phase between the oscillations in the real and imaginary components may prevent the violations of adiabaticity that have been argued to underly broad-band parametric resonance. In this paper, we give a treatment of parametric resonance for the decay of homogeneous complex scalar fields, analyzing properties of the resonance in the presence of out of phase oscillations of the real and imaginary components. For phase-invariant coupling of the driving parameter field to the decay field, and Mathieu type resonance, we give an explicit mapping from the complex resonance case to an equivalent real case with shifted resonance parameters. In addition, we consider the consequences of the complex field case as they apply to ``instant preheating,'' the explosive decay of non-convex potentials, and resonance in an expanding FRW universe. Applications of our considerations to supersymmetric cosmological models will be presented elsewhere.Comment: 20 pages, 2 figure