Catastrophic Particle Production under Periodic Perturbation

We develop a formalism to investigate the behavior of quantum field andquantum ground state when the field is coupled to perturbation thatperiodically oscillates. Working in the Schroedinger picture of quantum fieldtheory, we confirm that the phenomenon of parametric resonance in the classicaltheory implies an instability of quantum vacuum, and correspondingly it givesrise to catastrophic particle production if the oscillation lasts indefinitely;the produced number of particles exponentially increases without bound as timeproceeds. The density matrix describing the limiting stage of the quantum stateis determined by a small set of parameters. Moreover, the energy spectrum andthe intensity of produced particles are worked out in greatest detail in thelimit of weak coupling or small amplitude perturbation. In the case of strongcoupling or large amplitude perturbation the leading adiabatic formula isderived. Application to cosmological fate of weakly interacting spinless fields(WISF) such as the invisible axion, the Polonyi, and the modular fields isdiscussed. Although very little effect is expected on the invisible axion, thePolonyi type field has a chance that it catastrophically decays at an earlyepoch without much production of entropy, provided that an intrinsic couplingis large enough.Comment: 33 page