Related papers: Action on the Sphere: An Interfering Mean-Field Propagator for the Bose-Hubbard Dimer

Action on the Sphere: An Interfering Mean-Field Propagator for the Bose-Hubbard Dimer

URL: http://arxiv.org/abs/2606.30276v1
Date: Mon, 29 Jun 2026 13:22:22 GMT
Title: Action on the Sphere: An Interfering Mean-Field Propagator for the Bose-Hubbard Dimer
Abstract summary: The Bose-Hubbard system has been studied extensively both theoretically and experimentally.<n>We build on this to construct a simple initial-value coherent state propagator.<n>This yields an approximation to the full time-dependent many-particle state.
Score: 0.0
License: http://creativecommons.org/licenses/by/4.0/
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.

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