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 Tools annual

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 monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

We investigate the connection between energy level crossings in integrablesystems and their integrability, i.e. the existence of a set of non-trivialintegrals of motion. In particular, we consider a general quantum Hamiltonianlinear in the coupling u, H(u) = T + uV, and require that it has the maximumpossible number of nontrivial commuting partners also linear in u. Wedemonstrate how this commutation requirement alone leads to: (1) an exactsolution for the energy spectrum and (2) level crossings, which are alwayspresent in these Hamiltonians in violation of the Wigner-von Neumannnon-crossing rule. Moreover, we construct these Hamiltonians explicitly byresolving the above commutation requirement and show their equivalence to asector of Gaudin magnets (central spin Hamiltonians). In contrast, fewer thanthe maximum number of conservation laws does not guarantee level crossings.

The Link between Integrability, Level Crossings, and Exact Solution in Quantum Models