Action on the Sphere: An Interfering Mean-Field Propagator for the Bose-Hubbard Dimer
Abstract
The Bose-Hubbard system has been studied extensively both theoretically and experimentally, in particular in the context of ultracold atomic gases in optical lattices. Even in the two-mode case the many-particle dynamics display complex interference effects resulting in revival and breakdown phenomena as well as tunnelling. The most basic theoretical description is the mean-field approximation, which can be derived from a time-dependent variational principle assuming the many-particle wave function is an SU(2) coherent state. Here we build on this to construct a simple initial-value coherent state propagator, summing over mean-field trajectories and keeping track of their phases, given by the corresponding mean-field actions. This yields an approximation to the full time-dependent many-particle state, and is able to reproduce breakdown and revival dynamics. Applying a time-slicing procedure on top of this, we are able to accurately capture many-particle tunnelling effects. While in this paper we focus our analysis on the Bose-Hubbard dimer, the methods developed can be applied to more general SU(2) Hamiltonians, and can be extended to SU(M) systems.
Versions
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BibTeX
@misc{toddmiller2026action,
title = {{Action on the Sphere: An Interfering Mean-Field Propagator for the Bose-Hubbard Dimer}},
author = {Elana F Todd-Miller and Eva-Maria Graefe},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2606.30276},
eprint = {2606.30276},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.30276},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Action on the Sphere: An Interfering Mean-Field Propagator for the Bose-Hubbard Dimer
AU - Elana F Todd-Miller
AU - Eva-Maria Graefe
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2606.30276
UR - https://arxiv.org/abs/2606.30276
AB - The Bose-Hubbard system has been studied extensively both theoretically and experimentally, in particular in the context of ultracold atomic gases in optical lattices. Even in the two-mode case the many-particle dynamics display complex interference effects resulting in revival and breakdown phenomena as well as tunnelling. The most basic theoretical description is the mean-field approximation, which can be derived from a time-dependent variational principle assuming the many-particle wave function is an SU(2) coherent state. Here we build on this to construct a simple initial-value coherent state propagator, summing over mean-field trajectories and keeping track of their phases, given by the corresponding mean-field actions. This yields an approximation to the full time-dependent many-particle state, and is able to reproduce breakdown and revival dynamics. Applying a time-slicing procedure on top of this, we are able to accurately capture many-particle tunnelling effects. While in this paper we focus our analysis on the Bose-Hubbard dimer, the methods developed can be applied to more general SU(2) Hamiltonians, and can be extended to SU(M) systems.
ER -