Quantum Popcorn: the shape of a phase transition bubble
Abstract
A quantum tunneling event in field theory is usually depicted as the materialization of a spherical bubble of true vacuum. The bubble appears at rest, and its profile is the time-symmetric slice of Coleman's bounce, the Euclidean solution that controls the decay rate. However, the bubble is spherical only in the leading semiclassical approximation: at the next order the configuration is a Gaussian ensemble of fluctuations around the bounce. We derive the wave functional of the field on the nucleation slice from the half-bounce path integral, and use it to compute the root-mean-square quadrupole moment of a bubble at nucleation. The relative deformation of the bubble wall radius R is δR/R∼(ℏ/Sb)1/2, with Sb the bounce action. Thus δR/R∼0.1 for a typical cosmological phase transition with Sb/ℏ∼100.
Related
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BibTeX
@misc{blum2026quantum,
title = {{Quantum Popcorn: the shape of a phase transition bubble}},
author = {Kfir Blum and Ipak Fadakar and Omri Rosner and Guilherme L. Pimentel},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.41504},
eprint = {2610.41504},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.41504},
note = {CC0},
}
RIS
TY - UNPB
TI - Quantum Popcorn: the shape of a phase transition bubble
AU - Kfir Blum
AU - Ipak Fadakar
AU - Omri Rosner
AU - Guilherme L. Pimentel
PY - 2026
DA - 2026/10/30
PB - arXiv
DO - 10.48550/arxiv.2610.41504
UR - https://arxiv.org/abs/2610.41504
AB - A quantum tunneling event in field theory is usually depicted as the materialization of a spherical bubble of true vacuum. The bubble appears at rest, and its profile is the time-symmetric slice of Coleman's bounce, the Euclidean solution that controls the decay rate. However, the bubble is spherical only in the leading semiclassical approximation: at the next order the configuration is a Gaussian ensemble of fluctuations around the bounce. We derive the wave functional of the field on the nucleation slice from the half-bounce path integral, and use it to compute the root-mean-square quadrupole moment of a bubble at nucleation. The relative deformation of the bubble wall radius R is δR/R∼(ℏ/S_b)^1/2, with S_b the bounce action. Thus δR/R∼0.1 for a typical cosmological phase transition with S_b/ℏ∼100.
ER -