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 Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

Darboux's theorem guarantees the existence of local canonical coordinates onsymplectic manifolds under certain conditions. We demonstrate a general methodto construct such Darboux coordinates in the vicinity of a fixed point of anoncanonical Hamiltonian system via normal form expansions. The procedureserves as a tool to naturally extract canonical coordinates and at the sametime to transform the Hamiltonian into its Poincare-Birkhoff normal form. Themethod is general in the sense that it is applicable for arbitrary degrees offreedom, in arbitrary orders of the local expansion, and it is independent ofthe precise form of the Hamiltonian. The method presented allows for thegeneral and systematic investigation of noncanonical Hamiltonian systems in thevicinity of fixed points, which e.g. correspond to ground, excited ortransition states. As an exemplary field of application, we discuss avariational approach to quantum systems which defines a noncanonicalHamiltonian system for the variational parameters and which directly allows toapply transition state theory to quantum mechanical wave packets.

Construction of Darboux coordinates in noncanonical Hamiltonian systems via normal form expansions