Details
| Original language | English |
|---|---|
| Article number | 013801 |
| Number of pages | 7 |
| Journal | AVS Quantum Science |
| Volume | 7 |
| Issue number | 1 |
| Early online date | 3 Jan 2025 |
| Publication status | Published - Mar 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 subject areas
- Materials Science(all)
- Electronic, Optical and Magnetic Materials
- Physics and Astronomy(all)
- Atomic and Molecular Physics, and Optics
- Physics and Astronomy(all)
- Condensed Matter Physics
- Computer Science(all)
- Computer Networks and Communications
- Chemistry(all)
- Physical and Theoretical Chemistry
- Computer Science(all)
- Computational Theory and Mathematics
- Engineering(all)
- Electrical and Electronic Engineering
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In: AVS Quantum Science, Vol. 7, No. 1, 013801, 03.2025.
Research output: Contribution to journal › Article › Research › 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 -