Details
| Originalsprache | Englisch |
|---|---|
| Aufsatznummer | 013801 |
| Seitenumfang | 7 |
| Fachzeitschrift | AVS Quantum Science |
| Jahrgang | 7 |
| Ausgabenummer | 1 |
| Frühes Online-Datum | 3 Jan. 2025 |
| Publikationsstatus | Veröffentlicht - März 2025 |
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.
ASJC Scopus Sachgebiete
- Werkstoffwissenschaften (insg.)
- Elektronische, optische und magnetische Materialien
- Physik und Astronomie (insg.)
- Atom- und Molekularphysik sowie Optik
- Physik und Astronomie (insg.)
- Physik der kondensierten Materie
- Informatik (insg.)
- Computernetzwerke und -kommunikation
- Chemie (insg.)
- Physikalische und Theoretische Chemie
- Informatik (insg.)
- Theoretische Informatik und Mathematik
- Ingenieurwesen (insg.)
- Elektrotechnik und Elektronik
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in: AVS Quantum Science, Jahrgang 7, Nr. 1, 013801, 03.2025.
Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review
}
TY - JOUR
T1 - Resonance cascades and number theory
AU - Marchukov, Oleksandr V.
AU - Olshanii, Maxim
N1 - Publisher Copyright: © 2025 Author(s).
PY - 2025/3
Y1 - 2025/3
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85215549550&partnerID=8YFLogxK
U2 - 10.48550/arXiv.2402.04361
DO - 10.48550/arXiv.2402.04361
M3 - Article
AN - SCOPUS:85215549550
VL - 7
JO - AVS Quantum Science
JF - AVS Quantum Science
IS - 1
M1 - 013801
ER -