Time evolution of scalar condensate decay
Abstract
A scalar field, which oscillates coherently over the space and decays through production of daughter particles, plays an important role in cosmology. It was recently shown that the parametric-resonance and Feynman-diagrammatic approaches give the same decay rate for a Bosonic daughter particle at a large time duration. We study how the parametric-resonance result approaches to this asymptotic value, by numerically following the time evolution of the phase density of the daughter particle. We see a difference among different instability bands in the narrow-resonance regime. The lowest-order instability band approaches to the Feynman-diagrammatic result in tens of scalar oscillation periods, while the high-order instability bands approach dependently also on a coupling between the scalar and daughter particles. This would infer that the total decay width, to which the lowest-order instability band contributes most dominantly in the perturbation theory, approaches to the Feynman-diagrammatic result also independently of the coupling. To confirm it, we consider a simpler and analytically solvable quantum mechanical model: Rabi models. In the Bosonic Rabi model, the parametric-resonance and Feynman-diagrammatic results agree with each other for all the time. On the other hand, in the Fermionic Rabi model, they disagree at a large time duration. This difference would be attributed to Bose enhancement vs Pauli blocking.
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BibTeX
@misc{kamada2026time,
title = {{Time evolution of scalar condensate decay}},
author = {Ayuki Kamada and Kodai Sakurai},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.08420},
eprint = {2609.08420},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.08420},
note = {CC0},
}
RIS
TY - UNPB
TI - Time evolution of scalar condensate decay
AU - Ayuki Kamada
AU - Kodai Sakurai
PY - 2026
DA - 2026/09/08
PB - arXiv
DO - 10.48550/arxiv.2609.08420
UR - https://arxiv.org/abs/2609.08420
AB - A scalar field, which oscillates coherently over the space and decays through production of daughter particles, plays an important role in cosmology. It was recently shown that the parametric-resonance and Feynman-diagrammatic approaches give the same decay rate for a Bosonic daughter particle at a large time duration. We study how the parametric-resonance result approaches to this asymptotic value, by numerically following the time evolution of the phase density of the daughter particle. We see a difference among different instability bands in the narrow-resonance regime. The lowest-order instability band approaches to the Feynman-diagrammatic result in tens of scalar oscillation periods, while the high-order instability bands approach dependently also on a coupling between the scalar and daughter particles. This would infer that the total decay width, to which the lowest-order instability band contributes most dominantly in the perturbation theory, approaches to the Feynman-diagrammatic result also independently of the coupling. To confirm it, we consider a simpler and analytically solvable quantum mechanical model: Rabi models. In the Bosonic Rabi model, the parametric-resonance and Feynman-diagrammatic results agree with each other for all the time. On the other hand, in the Fermionic Rabi model, they disagree at a large time duration. This difference would be attributed to Bose enhancement vs Pauli blocking.
ER -