Resonance Cascades and Number Theory
Fuente:
arXiv
Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2024
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866915111353974784 |
|---|---|
| author | Marchukov, Oleksandr V. Olshanii, Maxim |
| author_facet | Marchukov, Oleksandr V. Olshanii, Maxim |
| contents | 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 [D. Cassettari, G. Mussardo and A. Trombettoni, PNAS Nexus {\bf 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_04361 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Resonance Cascades and Number Theory Marchukov, Oleksandr V. Olshanii, Maxim Quantum Gases 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 [D. Cassettari, G. Mussardo and A. Trombettoni, PNAS Nexus {\bf 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. |
| title | Resonance Cascades and Number Theory |
| topic | Quantum Gases |
| url | https://arxiv.org/abs/2402.04361 |