PreprintCC BY 4.0arXiv
Large particle number asymptotics for point-interacting bosons in the plane
Abstract
We consider N bosons in two dimensions interacting via point interactions, modeled by the TMS Hamiltonian. We prove that their ground state energy has the asymptotic behavior −eC N for large N, for an explicit constant C related to the sharp constant in the Ladyzhenskaya-Gagliardo-Nirenberg inequality. Such asymptotic behavior was predicted in the physics literature, based on a variant of the mean-field approximation.
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BibTeX
@misc{frank2026large,
title = {{Large particle number asymptotics for point-interacting bosons in the plane}},
author = {Rupert L. Frank and Robert Seiringer},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.06669},
eprint = {2611.06669},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.06669},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Large particle number asymptotics for point-interacting bosons in the plane
AU - Rupert L. Frank
AU - Robert Seiringer
PY - 2026
DA - 2026/11/04
PB - arXiv
DO - 10.48550/arxiv.2611.06669
UR - https://arxiv.org/abs/2611.06669
AB - We consider N bosons in two dimensions interacting via point interactions, modeled by the TMS Hamiltonian. We prove that their ground state energy has the asymptotic behavior −e^C N for large N, for an explicit constant C related to the sharp constant in the Ladyzhenskaya-Gagliardo-Nirenberg inequality. Such asymptotic behavior was predicted in the physics literature, based on a variant of the mean-field approximation.
ER -