Matches in SemOpenAlex for { <https://semopenalex.org/work/W3012295255> ?p ?o ?g. }
Showing items 1 to 71 of
71
with 100 items per page.
- W3012295255 abstract "Integral Apollonian packing, the packing of circles with integer curvatures, where every circle is tangent to three other mutually tangent circles, is shown to encode the fractal structure of the energy spectrum of two-dimensional Bloch electrons in a magnetic field, known as the Hofstadter butterfly. In this Apollonian-Butterfly-Connection, dubbed as $mathcal{ABC}$, the integer curvatures of the circles contain in a convoluted form, the topological quantum numbers of the butterfly graph -- the quanta of the Hall conductivity. Nesting properties of these two fractals are described in terms of the Apollonian group and the conformal transformations. The $mathcal{ABC}$ unfolds as the conformal maps describing butterfly recursions are related to the conformal maps describing nesting of circles in the Apollonian packing. Mapping of butterflies to Apollonian at all scales where Farey tree hierarchy plays the central role, reveals how geometry and number theory are intertwined in the quantum mechanics of Bloch electrons in a magnetic field." @default.
- W3012295255 created "2020-03-23" @default.
- W3012295255 creator A5014363562 @default.
- W3012295255 date "2020-03-11" @default.
- W3012295255 modified "2023-09-27" @default.
- W3012295255 title "What do Bloch Electrons in a Magnetic Field have to do with Apollonian packing of Circles" @default.
- W3012295255 cites W2001381069 @default.
- W3012295255 cites W2027823340 @default.
- W3012295255 cites W2031654810 @default.
- W3012295255 cites W2084401403 @default.
- W3012295255 cites W2090268658 @default.
- W3012295255 cites W2107025564 @default.
- W3012295255 cites W2127627418 @default.
- W3012295255 cites W2465287539 @default.
- W3012295255 cites W2514569774 @default.
- W3012295255 cites W3175367423 @default.
- W3012295255 hasPublicationYear "2020" @default.
- W3012295255 type Work @default.
- W3012295255 sameAs 3012295255 @default.
- W3012295255 citedByCount "0" @default.
- W3012295255 crossrefType "posted-content" @default.
- W3012295255 hasAuthorship W3012295255A5014363562 @default.
- W3012295255 hasConcept C114614502 @default.
- W3012295255 hasConcept C115260700 @default.
- W3012295255 hasConcept C121332964 @default.
- W3012295255 hasConcept C123115066 @default.
- W3012295255 hasConcept C173734053 @default.
- W3012295255 hasConcept C200369452 @default.
- W3012295255 hasConcept C2524010 @default.
- W3012295255 hasConcept C33923547 @default.
- W3012295255 hasConcept C37914503 @default.
- W3012295255 hasConcept C62520636 @default.
- W3012295255 hasConcept C98214594 @default.
- W3012295255 hasConceptScore W3012295255C114614502 @default.
- W3012295255 hasConceptScore W3012295255C115260700 @default.
- W3012295255 hasConceptScore W3012295255C121332964 @default.
- W3012295255 hasConceptScore W3012295255C123115066 @default.
- W3012295255 hasConceptScore W3012295255C173734053 @default.
- W3012295255 hasConceptScore W3012295255C200369452 @default.
- W3012295255 hasConceptScore W3012295255C2524010 @default.
- W3012295255 hasConceptScore W3012295255C33923547 @default.
- W3012295255 hasConceptScore W3012295255C37914503 @default.
- W3012295255 hasConceptScore W3012295255C62520636 @default.
- W3012295255 hasConceptScore W3012295255C98214594 @default.
- W3012295255 hasLocation W30122952551 @default.
- W3012295255 hasOpenAccess W3012295255 @default.
- W3012295255 hasPrimaryLocation W30122952551 @default.
- W3012295255 hasRelatedWork W1659581999 @default.
- W3012295255 hasRelatedWork W1963648551 @default.
- W3012295255 hasRelatedWork W2006376439 @default.
- W3012295255 hasRelatedWork W2249498138 @default.
- W3012295255 hasRelatedWork W2300773149 @default.
- W3012295255 hasRelatedWork W2306294985 @default.
- W3012295255 hasRelatedWork W2465287539 @default.
- W3012295255 hasRelatedWork W2948333742 @default.
- W3012295255 hasRelatedWork W2950923296 @default.
- W3012295255 hasRelatedWork W3010937115 @default.
- W3012295255 hasRelatedWork W3044236720 @default.
- W3012295255 hasRelatedWork W3095633689 @default.
- W3012295255 hasRelatedWork W3105556393 @default.
- W3012295255 hasRelatedWork W3105619010 @default.
- W3012295255 hasRelatedWork W3106405632 @default.
- W3012295255 hasRelatedWork W3128314877 @default.
- W3012295255 hasRelatedWork W3176856489 @default.
- W3012295255 hasRelatedWork W3205009679 @default.
- W3012295255 hasRelatedWork W4229004457 @default.
- W3012295255 hasRelatedWork W966347339 @default.
- W3012295255 isParatext "false" @default.
- W3012295255 isRetracted "false" @default.
- W3012295255 magId "3012295255" @default.
- W3012295255 workType "article" @default.