English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Adiabatic approximations are a powerful tool for simplifying nonlinearquantum dynamics, and are applicable whenever a system exhibits a hierarchy oftime scales. Current interest in small nonlinear quantum systems, such asfew-mode Bose-Hubbard models, warrants further development of adiabatic methodsin the particular context of these models. Here we extend our recent work on asimple four-mode Bose-Hubbard model with two distinct dynamical time scales, inwhich we showed that among the perturbations around excited stationary statesof the system is a slow collective excitation that is not present in theBogoliubov spectrum. We characterized this mode as a resonant energy exchangewith its frequency shifted by nonlinear effects, and referred to it as a secondJosephson oscillation, in analogy with the second sound mode of liquid heliumII. We now generalize our previous theory beyond the mean field regime, andconstruct a general Bogoliubov free quasiparticle theory that explicitlyrespects the system's adiabatic invariant as well the exact conservation ofparticles. We compare this theory to the numerically exact quantum energyspectrum with up to forty particles, and find good agreement over a significantrange of parameter space.

An extension of Bogoliubov theory for a many-body system with a time scale hierarchy: the quantum mechanics of second Josephson oscillations