Action on the sphere: an interfering mean-field propagator for the Bose-Hubbard dimer
File(s)
Author(s)
Todd-Miller, Elana
Graefe, Eva-Maria
Type
Journal Article
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.
Date Issued
2026-09-03
Date Acceptance
2026-09-03
Citation
Journal of Physics A: Mathematical and Theoretical, 2026
ISSN
1751-8113
Publisher
IOP Publishing
Journal / Book Title
Journal of Physics A: Mathematical and Theoretical
Copyright Statement
As the Version of Record of this article is going to be / has been published on a gold open access basis under a CC BY 4.0 licence, this Accepted Manuscript is available for reuse under a CC BY 4.0 licence immediately. Everyone is permitted to use all or part of the original content in this article, provided that they adhere to all the terms of the licence https://creativecommons.org/licences/by/4.0
License URL
Identifier
10.1088/1751-8121/aea277
Subjects
Bose-Hubbard dimer
semiclassical methods
SU(2) coherent states
Publication Status
Published online
Date Publish Online
2026-09-03