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

We study the mixed-type classical dynamics of the three-particleFermi-Pasta-Ulam-Tsingou (FPUT) model in relationship with its quantumcounterpart, and present new results on aspects of quantum chaos in thissystem. First we derive for the general N-particle FPUT system thetransformation to the normal mode representation. Then we specialize to thethree-particle FPUT case, and derive analytically the semiclassical energydensity of states, and its derivatives in which different singularies aredetermined, using the Thomas-Fermi rule. The result perfectly agrees with thenumerical energy density from the Krylov subspace method, as well as with theenergy density obtained by the method of quantum typicality. Here, in paper I,we concentrate on the energy level statistics (level spacing and spacingratios), in all classical dynamical regimes of interest: the almost entirelyregular, the entirely chaotic, and the mixed-type regimes. We clearly confirm,correspondingly, the Poissonian statistics, the GOE statistics, and theBerry-Robnik-Brody (BRB) statistics in the mixed-type regime. It is found thatthe BRB level spacing distribution perfectly fits the numerical data. Theextracted quantum Berry-Robnik parameter is found to agree with the classicalvalue within better than one percent. We discuss the role of localization ofchaotic eigenstates, and its appearances, in relation to the classical phasespace structure (Poincar\'e and SALI plots), whose details will be presented inpaper II, where the structure and the statistical properties of the Husimifunctions in the quantum phase space will be studied.

Chaos and quantization of the three-particle generic Fermi-Pasta-Ulam-Tsingou model I: Density of states and spectral statistics