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Nonlocal Cubic Density Gibbs Measures from Bosonic Gibbs States with Three-Body Interactions
Abstract
We study the high-temperature mean-field limit of grand-canonical bosonic Gibbs states on the torus with renormalized nonlocal three-body interactions. In dimensions two and three, we construct the limiting nonlinear classical Gibbs measure and prove convergence of the relative free energy and of the reduced density matrices of every fixed order; in three dimensions, a smallness condition on the interaction is imposed. The proof combines the density-channel representation of the interaction with a coherent-state variational method based on the upper-symbol representation of the free Gibbs state. The same framework also contains, as a special case, the homogeneous positive-type model studied by Lewin, Nam, and Rougerie (2021).
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BibTeX
@misc{liang2026nonlocal,
title = {{Nonlocal Cubic Density Gibbs Measures from Bosonic Gibbs States with Three-Body Interactions}},
author = {Hao Liang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2607.23041},
eprint = {2607.23041},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.23041},
}
RIS
TY - UNPB
TI - Nonlocal Cubic Density Gibbs Measures from Bosonic Gibbs States with Three-Body Interactions
AU - Hao Liang
PY - 2026
DA - 2026/09/22
PB - arXiv
DO - 10.48550/arxiv.2607.23041
UR - https://arxiv.org/abs/2607.23041
AB - We study the high-temperature mean-field limit of grand-canonical bosonic Gibbs states on the torus with renormalized nonlocal three-body interactions. In dimensions two and three, we construct the limiting nonlinear classical Gibbs measure and prove convergence of the relative free energy and of the reduced density matrices of every fixed order; in three dimensions, a smallness condition on the interaction is imposed. The proof combines the density-channel representation of the interaction with a coherent-state variational method based on the upper-symbol representation of the free Gibbs state. The same framework also contains, as a special case, the homogeneous positive-type model studied by Lewin, Nam, and Rougerie (2021).
ER -