Scaling equations for Bose-Einstein condensate dynamics across all interaction regimes
Abstract
We derive a unified set of scaling equations for Bose-Einstein condensates in time-dependent harmonic traps, connecting the weakly interacting Gaussian regime to the strongly interacting Thomas-Fermi regime. The exact Gross-Pitaevskii ground-state density is taken as a fixed profile in rescaled coordinates, with its dynamics described by three scaling factors corresponding to compression or expansion along the three spatial directions. The resulting equations contain no adjustable parameter, since their coefficients are determined once from the initial state. They recover analytically the Gaussian variational and Thomas-Fermi scaling equations in their respective limits and satisfy an axis-resolved virial theorem. The approach also yields the global phase and the low-lying collective-mode frequencies of the condensate. We benchmark the model against three-dimensional Gross-Pitaevskii simulations and against measured expansion energies. The model remains accurate across all interaction regimes, in strongly anisotropic traps, and along time-dependent sequences including a relatively fast quench, up to the point where the underlying frozen-profile hypothesis, shared by all three scaling approaches, breaks down.
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BibTeX
@misc{marinica2026scaling,
title = {{Scaling equations for Bose-Einstein condensate dynamics across all interaction regimes}},
author = {D. C. Marinica and C. Puertas González and T. Estrampes and A. Herbst and D. Schlippert and E. M. Rasel and N. Gaaloul and E. Charron},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.13497},
eprint = {2609.13497},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.13497},
}
RIS
TY - UNPB
TI - Scaling equations for Bose-Einstein condensate dynamics across all interaction regimes
AU - D. C. Marinica
AU - C. Puertas González
AU - T. Estrampes
AU - A. Herbst
AU - D. Schlippert
AU - E. M. Rasel
AU - N. Gaaloul
AU - E. Charron
PY - 2026
DA - 2026/10/02
PB - arXiv
DO - 10.48550/arxiv.2609.13497
UR - https://arxiv.org/abs/2609.13497
AB - We derive a unified set of scaling equations for Bose-Einstein condensates in time-dependent harmonic traps, connecting the weakly interacting Gaussian regime to the strongly interacting Thomas-Fermi regime. The exact Gross-Pitaevskii ground-state density is taken as a fixed profile in rescaled coordinates, with its dynamics described by three scaling factors corresponding to compression or expansion along the three spatial directions. The resulting equations contain no adjustable parameter, since their coefficients are determined once from the initial state. They recover analytically the Gaussian variational and Thomas-Fermi scaling equations in their respective limits and satisfy an axis-resolved virial theorem. The approach also yields the global phase and the low-lying collective-mode frequencies of the condensate. We benchmark the model against three-dimensional Gross-Pitaevskii simulations and against measured expansion energies. The model remains accurate across all interaction regimes, in strongly anisotropic traps, and along time-dependent sequences including a relatively fast quench, up to the point where the underlying frozen-profile hypothesis, shared by all three scaling approaches, breaks down.
ER -