Resonance cascades and number theory

verfasst von: Oleksandr V. Marchukov, Maxim Olshanii
Abstract: In this article, we are interested in situations where the existence of a contiguous cascade of quantum resonant transitions is predicated on the validity of a particular statement in number theory. The setting is a tailored one-atom one-dimensional potential with a prescribed spectrum under a weak periodic perturbation. The former is, by now, an experimental reality [Cassettari et al., PNAS Nexus 2, pgac279 (2022)]. As a case study, we look at the following trivial statement: “Any power of 3 is an integer.” Consequently, we “test” this statement in a numerical experiment where we demonstrate an unimpeded upward mobility along an equidistant ln ( 3 ) -spaced subsequence of the energy levels of a potential with a log-natural spectrum under a frequency ln ( 3 ) time-periodic perturbation. We further show that when we “remove” 9 from the set of integers—by excluding the corresponding energy level from the spectrum—the cascade halts abruptly.
Organisationseinheit(en): Institut für Photonik
Externe Organisation(en): Technische Universität Darmstadt
University of Massachusetts Boston
Typ: Artikel
Journal: AVS Quantum Science
Band: 7
Anzahl der Seiten: 7
Publikationsdatum: 03.2025
Publikationsstatus: Veröffentlicht
Peer-reviewed: Ja
ASJC Scopus Sachgebiete: Elektronische, optische und magnetische Materialien, Atom- und Molekularphysik sowie Optik, Physik der kondensierten Materie, Computernetzwerke und -kommunikation, Physikalische und Theoretische Chemie, Theoretische Informatik und Mathematik, Elektrotechnik und Elektronik
Elektronische Version(en): https://doi.org/10.48550/arXiv.2402.04361 (Zugang: Offen)
https://doi.org/10.1116/5.0232065 (Zugang: Geschlossen)

BibTeX

@article{4121293447a941a78bf0a476e4a6a8bf,
title = "Resonance cascades and number theory",
abstract = "In this article, we are interested in situations where the existence of a contiguous cascade of quantum resonant transitions is predicated on the validity of a particular statement in number theory. The setting is a tailored one-atom one-dimensional potential with a prescribed spectrum under a weak periodic perturbation. The former is, by now, an experimental reality [Cassettari et al., PNAS Nexus 2, pgac279 (2022)]. As a case study, we look at the following trivial statement: “Any power of 3 is an integer.” Consequently, we “test” this statement in a numerical experiment where we demonstrate an unimpeded upward mobility along an equidistant ln ( 3 ) -spaced subsequence of the energy levels of a potential with a log-natural spectrum under a frequency ln ( 3 ) time-periodic perturbation. We further show that when we “remove” 9 from the set of integers—by excluding the corresponding energy level from the spectrum—the cascade halts abruptly.",
author = "Marchukov, {Oleksandr V.} and Maxim Olshanii",
note = "Publisher Copyright: {\textcopyright} 2025 Author(s).",
year = "2025",
month = mar,
doi = "10.48550/arXiv.2402.04361",
language = "English",
volume = "7",
journal = "AVS Quantum Science",
issn = "2639-0213",
publisher = "American Institute of Physics",
number = "1",
}