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Dynamics of two-dimensional Bose gases in the focusing case
Abstract
We prove the propagation of Bose--Einstein condensation and a norm approximation for the dynamics of a Bose gas with localized initial data in two dimensions with singular interactions that may have a small attractive part. We allow the scaling of the interaction to be any polynomial scaling Nβ for 0<β<∞ and even exponential scaling eNκ for 0<κ<1/4. Our approach covers external potentials that are time-dependent, at most quadratic, and bounded below, including the situation without an external potential.
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BibTeX
@misc{reichmann2026dynamics,
title = {{Dynamics of two-dimensional Bose gases in the focusing case}},
author = {Lukas Reichmann},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.33212},
eprint = {2610.33212},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.33212},
}
RIS
TY - UNPB
TI - Dynamics of two-dimensional Bose gases in the focusing case
AU - Lukas Reichmann
PY - 2026
DA - 2026/10/23
PB - arXiv
DO - 10.48550/arxiv.2610.33212
UR - https://arxiv.org/abs/2610.33212
AB - We prove the propagation of Bose--Einstein condensation and a norm approximation for the dynamics of a Bose gas with localized initial data in two dimensions with singular interactions that may have a small attractive part. We allow the scaling of the interaction to be any polynomial scaling N^β for 0<β<∞ and even exponential scaling e^N^κ for 0<κ<1/4. Our approach covers external potentials that are time-dependent, at most quadratic, and bounded below, including the situation without an external potential.
ER -