{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,8]],"date-time":"2026-06-08T23:05:55Z","timestamp":1780959955667,"version":"3.54.1"},"reference-count":33,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2023,3,21]],"date-time":"2023-03-21T00:00:00Z","timestamp":1679356800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"MUR Italy","award":["201798CZL"],"award-info":[{"award-number":["201798CZL"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>We study the transition from integrability to chaos for the three-particle Fermi\u2013Pasta\u2013Ulam\u2013Tsingou (FPUT) model. We can show that both the quartic \u03b2-FPUT model (\u03b1=0) and the cubic one (\u03b2=0) are integrable by introducing an appropriate Fourier representation to express the nonlinear terms of the Hamiltonian. For generic values of \u03b1 and \u03b2, the model is non-integrable and displays a mixed phase space with both chaotic and regular trajectories. In the classical case, chaos is diagnosed by the investigation of Poincar\u00e9 sections. In the quantum case, the level spacing statistics in the energy basis belongs to the Gaussian orthogonal ensemble in the chaotic regime, and crosses over to Poissonian behavior in the quasi-integrable low-energy limit. In the chaotic part of the spectrum, two generic observables obey the eigenstate thermalization hypothesis.<\/jats:p>","DOI":"10.3390\/e25030538","type":"journal-article","created":{"date-parts":[[2023,3,21]],"date-time":"2023-03-21T06:56:48Z","timestamp":1679381808000},"page":"538","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Quantization of Integrable and Chaotic Three-Particle Fermi\u2013Pasta\u2013Ulam\u2013Tsingou Models"],"prefix":"10.3390","volume":"25","author":[{"given":"Alio Issoufou","family":"Arzika","sequence":"first","affiliation":[{"name":"LCEMR, Faculty of Science and Technology, Abdou Moumouni University, Niamey BP 10662, Niger"},{"name":"SISSA, Via Bonomea 265, 34136 Trieste, Italy"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Andrea","family":"Solfanelli","sequence":"additional","affiliation":[{"name":"SISSA, Via Bonomea 265, 34136 Trieste, Italy"},{"name":"INFN, Sezione di Trieste, Via Valerio 2, 34127 Trieste, Italy"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Harald","family":"Schmid","sequence":"additional","affiliation":[{"name":"Dahlem Center for Complex Quantum Systems, Freie Universit\u00e4t Berlin, 14195 Berlin, Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2911-8718","authenticated-orcid":false,"given":"Stefano","family":"Ruffo","sequence":"additional","affiliation":[{"name":"SISSA, Via Bonomea 265, 34136 Trieste, Italy"},{"name":"INFN, Sezione di Trieste, Via Valerio 2, 34127 Trieste, Italy"},{"name":"Istituto dei Sistemi Complessi, Via Madonna del Piano 10, 50019 Sesto Fiorentino, Italy"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2023,3,21]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Fermi, E., Pasta, J., Ulam, S., and Tsingou, M. 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