FRINK Linked Data Fragments server

Matches in SemOpenAlex for { <https://semopenalex.org/work/W2279121569> ?p ?o ?g. }

• W2279121569 endingPage "1183" @default.
• W2279121569 startingPage "1147" @default.
• W2279121569 abstract "We study the scaling asymptotics of the eigenspace projection kernels $Pi_{hbar, E}(x,y)$ of the isotropic Harmonic Oscillator $- hbar ^2 Delta + |x|^2$ of eigenvalue $E = hbar(N + frac{d}{2})$ in the semi-classical limit $hbar to 0$. The principal result is an explicit formula for the scaling asymptotics of $Pi_{hbar, E}(x,y)$ for $x,y$ in a $hbar^{2/3}$ neighborhood of the caustic $mathcal C_E$ as $hbar to 0.$ The scaling asymptotics are applied to the distribution of nodal sets of Gaussian random eigenfunctions around the caustic as $hbar to 0$. In previous work we proved that the density of zeros of Gaussian random eigenfunctions of $hat{H}_{hbar}$ have different orders in the Planck constant $hbar$ in the allowed and forbidden regions: In the allowed region the density is of order $hbar^{-1}$ while it is $hbar^{-1/2}$ in the forbidden region. Our main result on nodal sets is that the density of zeros is of order $hbar^{-frac{2}{3}}$ in an $hbar^{frac{2}{3}}$-tube around the caustic. This tube radius is the `critical radius'. For annuli of larger inner and outer radii $hbar^{alpha}$ with $0< alpha < frac{2}{3}$ we obtain density results which interpolate between this critical radius result and our prior ones in the allowed and forbidden region. We also show that the Hausdorff $(d-2)$-dimensional measure of the intersection of the nodal set with the caustic is of order $hbar^{- frac{2}{3}}$." @default.
• W2279121569 created "2016-06-24" @default.
• W2279121569 creator A5021132688 @default.
• W2279121569 creator A5051556693 @default.
• W2279121569 creator A5085872076 @default.
• W2279121569 date "2016-12-01" @default.
• W2279121569 modified "2023-09-24" @default.
• W2279121569 title "Scaling of Harmonic Oscillator Eigenfunctions and Their Nodal Sets Around the Caustic" @default.
• W2279121569 cites W171105080 @default.
• W2279121569 cites W1967640295 @default.
• W2279121569 cites W1986280275 @default.
• W2279121569 cites W2000510735 @default.
• W2279121569 cites W2016326733 @default.
• W2279121569 cites W2025082090 @default.
• W2279121569 cites W2029821064 @default.
• W2279121569 cites W2086276479 @default.
• W2279121569 cites W2087304141 @default.
• W2279121569 cites W2090432663 @default.
• W2279121569 cites W2123485948 @default.
• W2279121569 cites W2132280235 @default.
• W2279121569 cites W2170751889 @default.
• W2279121569 cites W2499952289 @default.
• W2279121569 cites W2567165719 @default.
• W2279121569 cites W3036926079 @default.
• W2279121569 cites W3104692534 @default.
• W2279121569 cites W4244869027 @default.
• W2279121569 cites W577213760 @default.
• W2279121569 cites W75600330 @default.
• W2279121569 doi "https://doi.org/10.1007/s00220-016-2807-4" @default.
• W2279121569 hasPublicationYear "2016" @default.
• W2279121569 type Work @default.
• W2279121569 sameAs 2279121569 @default.
• W2279121569 citedByCount "4" @default.
• W2279121569 countsByYear W22791215692018 @default.
• W2279121569 countsByYear W22791215692019 @default.
• W2279121569 countsByYear W22791215692020 @default.
• W2279121569 countsByYear W22791215692022 @default.
• W2279121569 crossrefType "journal-article" @default.
• W2279121569 hasAuthorship W2279121569A5021132688 @default.
• W2279121569 hasAuthorship W2279121569A5051556693 @default.
• W2279121569 hasAuthorship W2279121569A5085872076 @default.
• W2279121569 hasBestOaLocation W22791215692 @default.
• W2279121569 hasConcept C10138342 @default.
• W2279121569 hasConcept C114614502 @default.
• W2279121569 hasConcept C121332964 @default.
• W2279121569 hasConcept C128803854 @default.
• W2279121569 hasConcept C134306372 @default.
• W2279121569 hasConcept C158693339 @default.
• W2279121569 hasConcept C162324750 @default.
• W2279121569 hasConcept C178635117 @default.
• W2279121569 hasConcept C182306322 @default.
• W2279121569 hasConcept C2524010 @default.
• W2279121569 hasConcept C2779567845 @default.
• W2279121569 hasConcept C33923547 @default.
• W2279121569 hasConcept C37914503 @default.
• W2279121569 hasConcept C38652104 @default.
• W2279121569 hasConcept C40934718 @default.
• W2279121569 hasConcept C41008148 @default.
• W2279121569 hasConcept C62520636 @default.
• W2279121569 hasConcept C99844830 @default.
• W2279121569 hasConceptScore W2279121569C10138342 @default.
• W2279121569 hasConceptScore W2279121569C114614502 @default.
• W2279121569 hasConceptScore W2279121569C121332964 @default.
• W2279121569 hasConceptScore W2279121569C128803854 @default.
• W2279121569 hasConceptScore W2279121569C134306372 @default.
• W2279121569 hasConceptScore W2279121569C158693339 @default.
• W2279121569 hasConceptScore W2279121569C162324750 @default.
• W2279121569 hasConceptScore W2279121569C178635117 @default.
• W2279121569 hasConceptScore W2279121569C182306322 @default.
• W2279121569 hasConceptScore W2279121569C2524010 @default.
• W2279121569 hasConceptScore W2279121569C2779567845 @default.
• W2279121569 hasConceptScore W2279121569C33923547 @default.
• W2279121569 hasConceptScore W2279121569C37914503 @default.
• W2279121569 hasConceptScore W2279121569C38652104 @default.
• W2279121569 hasConceptScore W2279121569C40934718 @default.
• W2279121569 hasConceptScore W2279121569C41008148 @default.
• W2279121569 hasConceptScore W2279121569C62520636 @default.
• W2279121569 hasConceptScore W2279121569C99844830 @default.
• W2279121569 hasFunder F4320337380 @default.
• W2279121569 hasIssue "3" @default.
• W2279121569 hasLocation W22791215691 @default.
• W2279121569 hasLocation W22791215692 @default.
• W2279121569 hasLocation W22791215693 @default.
• W2279121569 hasOpenAccess W2279121569 @default.
• W2279121569 hasPrimaryLocation W22791215691 @default.
• W2279121569 hasRelatedWork W1567649440 @default.
• W2279121569 hasRelatedWork W1976128076 @default.
• W2279121569 hasRelatedWork W1988470747 @default.
• W2279121569 hasRelatedWork W2006061546 @default.
• W2279121569 hasRelatedWork W2079338193 @default.
• W2279121569 hasRelatedWork W2371806783 @default.
• W2279121569 hasRelatedWork W2811355396 @default.
• W2279121569 hasRelatedWork W2950533787 @default.
• W2279121569 hasRelatedWork W3190750625 @default.
• W2279121569 hasRelatedWork W4285712201 @default.
• W2279121569 hasVolume "350" @default.
• W2279121569 isParatext "false" @default.
• W2279121569 isRetracted "false" @default.

• next