Matches in SemOpenAlex for { <https://semopenalex.org/work/W4287759137> ?p ?o ?g. }
Showing items 1 to 61 of
61
with 100 items per page.
- W4287759137 abstract "We study the statistical properties of the spacings between neighboring energy levels for the multi-dimensional quantum harmonic oscillator that occur in a window $[E,E+Delta E)$ of fixed width $Delta E$ as $E$ tends to infinity. This regime provides a notable exception to the Berry-Tabor Conjecture from Quantum Chaos and, for that reason, it was studied extensively by Berry and Tabor in their seminal paper from 1977. We focus entirely on the case that the (ratios of) frequencies $omega_1,omega_2,ldots,omega_d$ together with $1$ form a basis for an algebraic number field $Phi$ of degree $d+1$, allowing us to use tools from algebraic number theory. This special case was studied by Dyson, Bleher, Bleher-Homma-Ji-Roeder-Shen, and others. Under a suitable rescaling, we prove that the distribution of spacings behaves asymptotically quasiperiodically in $log E$. We also prove that the distribution of ratios of neighboring spacings behaves asymptotically quasiperiodically in $log E$. The same holds for the distribution of finite words in the finite alphabet of rescaled spacings. Mathematically, our work is a higher dimensional version of the Steinhaus Conjecture (Three Gap Theorem) involving the fractional parts of a linear form in more than one variable, and it is of independent interest from this perspective." @default.
- W4287759137 created "2022-07-26" @default.
- W4287759137 creator A5020433531 @default.
- W4287759137 creator A5079771152 @default.
- W4287759137 date "2020-06-10" @default.
- W4287759137 modified "2023-09-30" @default.
- W4287759137 title "Level spacing statistics for the multi-dimensional quantum harmonic oscillator: algebraic case" @default.
- W4287759137 doi "https://doi.org/10.48550/arxiv.2006.06157" @default.
- W4287759137 hasPublicationYear "2020" @default.
- W4287759137 type Work @default.
- W4287759137 citedByCount "0" @default.
- W4287759137 crossrefType "posted-content" @default.
- W4287759137 hasAuthorship W4287759137A5020433531 @default.
- W4287759137 hasAuthorship W4287759137A5079771152 @default.
- W4287759137 hasBestOaLocation W42877591371 @default.
- W4287759137 hasConcept C110121322 @default.
- W4287759137 hasConcept C114614502 @default.
- W4287759137 hasConcept C121332964 @default.
- W4287759137 hasConcept C122332657 @default.
- W4287759137 hasConcept C134306372 @default.
- W4287759137 hasConcept C202444582 @default.
- W4287759137 hasConcept C2779557605 @default.
- W4287759137 hasConcept C2780990831 @default.
- W4287759137 hasConcept C33923547 @default.
- W4287759137 hasConcept C37914503 @default.
- W4287759137 hasConcept C40934718 @default.
- W4287759137 hasConcept C62520636 @default.
- W4287759137 hasConcept C7321624 @default.
- W4287759137 hasConcept C84114770 @default.
- W4287759137 hasConcept C9376300 @default.
- W4287759137 hasConceptScore W4287759137C110121322 @default.
- W4287759137 hasConceptScore W4287759137C114614502 @default.
- W4287759137 hasConceptScore W4287759137C121332964 @default.
- W4287759137 hasConceptScore W4287759137C122332657 @default.
- W4287759137 hasConceptScore W4287759137C134306372 @default.
- W4287759137 hasConceptScore W4287759137C202444582 @default.
- W4287759137 hasConceptScore W4287759137C2779557605 @default.
- W4287759137 hasConceptScore W4287759137C2780990831 @default.
- W4287759137 hasConceptScore W4287759137C33923547 @default.
- W4287759137 hasConceptScore W4287759137C37914503 @default.
- W4287759137 hasConceptScore W4287759137C40934718 @default.
- W4287759137 hasConceptScore W4287759137C62520636 @default.
- W4287759137 hasConceptScore W4287759137C7321624 @default.
- W4287759137 hasConceptScore W4287759137C84114770 @default.
- W4287759137 hasConceptScore W4287759137C9376300 @default.
- W4287759137 hasLocation W42877591371 @default.
- W4287759137 hasOpenAccess W4287759137 @default.
- W4287759137 hasPrimaryLocation W42877591371 @default.
- W4287759137 hasRelatedWork W1660642588 @default.
- W4287759137 hasRelatedWork W2027534011 @default.
- W4287759137 hasRelatedWork W2466470134 @default.
- W4287759137 hasRelatedWork W2897153210 @default.
- W4287759137 hasRelatedWork W2951462276 @default.
- W4287759137 hasRelatedWork W3000713236 @default.
- W4287759137 hasRelatedWork W3026358768 @default.
- W4287759137 hasRelatedWork W3101827008 @default.
- W4287759137 hasRelatedWork W3134390824 @default.
- W4287759137 hasRelatedWork W4320926309 @default.
- W4287759137 isParatext "false" @default.
- W4287759137 isRetracted "false" @default.
- W4287759137 workType "article" @default.