Measure-valued free-energy minimizers for trapped bosons with repulsive Coulomb interaction
Abstract
We study a free-energy minimization problem for a trapped semiclassical Bose gas with repulsive Coulomb self-interaction. Because the bosonic entropy density has zero recession slope, the natural relaxation is posed over nonnegative finite Radon measures on phase space, and a minimizer may have a singular component. We interpret this component as condensation within the relaxed semiclassical model. We prove existence and uniqueness at every positive temperature, derive the Euler-Lagrange contact condition and an obstacle-type formula for the condensed density, and establish sharp phase boundaries under only the standing continuity assumptions on the trap. At fixed mass there is a unique finite positive critical temperature, with condensation precisely below it. At fixed temperature there is a sharp critical mass, possibly infinite, separating normal and condensed minimizers. For harmonic traps we obtain a sharp confinement-strength dichotomy. We also prove an abstract conditional variational-stability statement for measure-valued curves that conserve mass and satisfy the free-energy inequality.
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BibTeX
@misc{bae2026measurevalued,
title = {{Measure-valued free-energy minimizers for trapped bosons with repulsive Coulomb interaction}},
author = {Gi-Chan Bae and Jinmyoung Seok},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2608.26900},
eprint = {2608.26900},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.26900},
}
RIS
TY - UNPB
TI - Measure-valued free-energy minimizers for trapped bosons with repulsive Coulomb interaction
AU - Gi-Chan Bae
AU - Jinmyoung Seok
PY - 2026
DA - 2026/09/06
PB - arXiv
DO - 10.48550/arxiv.2608.26900
UR - https://arxiv.org/abs/2608.26900
AB - We study a free-energy minimization problem for a trapped semiclassical Bose gas with repulsive Coulomb self-interaction. Because the bosonic entropy density has zero recession slope, the natural relaxation is posed over nonnegative finite Radon measures on phase space, and a minimizer may have a singular component. We interpret this component as condensation within the relaxed semiclassical model. We prove existence and uniqueness at every positive temperature, derive the Euler-Lagrange contact condition and an obstacle-type formula for the condensed density, and establish sharp phase boundaries under only the standing continuity assumptions on the trap. At fixed mass there is a unique finite positive critical temperature, with condensation precisely below it. At fixed temperature there is a sharp critical mass, possibly infinite, separating normal and condensed minimizers. For harmonic traps we obtain a sharp confinement-strength dichotomy. We also prove an abstract conditional variational-stability statement for measure-valued curves that conserve mass and satisfy the free-energy inequality.
ER -