Catastrophic Particle Production under Periodic Perturbation

TL;DR

This paper develops a formalism to analyze quantum field behavior under periodic perturbations, revealing that parametric resonance leads to exponential particle production and potential cosmological implications for certain fields.

Contribution

It introduces a quantum formalism for periodic perturbations, detailing particle production mechanisms and applying findings to cosmological fields like axions and Polonyi.

Findings

Quantum vacuum becomes unstable under periodic perturbation.

Particle number grows exponentially with time during resonance.

Weak coupling results are detailed; strong coupling uses adiabatic approximation.

Abstract

We develop a formalism to investigate the behavior of quantum field and quantum ground state when the field is coupled to perturbation that periodically oscillates. Working in the Schroedinger picture of quantum field theory, we confirm that the phenomenon of parametric resonance in the classical theory implies an instability of quantum vacuum, and correspondingly it gives rise to catastrophic particle production if the oscillation lasts indefinitely; the produced number of particles exponentially increases without bound as time proceeds. The density matrix describing the limiting stage of the quantum state is determined by a small set of parameters. Moreover, the energy spectrum and the intensity of produced particles are worked out in greatest detail in the limit of weak coupling or small amplitude perturbation. In the case of strong coupling or large amplitude perturbation the leading adiabatic formula is derived. Application to cosmological fate of weakly interacting spinless fields (WISF) such as the invisible axion, the Polonyi, and the modular fields is discussed. Although very little effect is expected on the invisible axion, the Polonyi type field has a chance that it catastrophically decays at an early epoch without much production of entropy, provided that an intrinsic coupling is large enough.