Symmetry of emission spectra of dual convex polyhedra

Autor:	Richard L. Liboff
Rok vydání:	2004
Předmět:	Convex hull Physics Convex analysis Polyhedron Pure mathematics Regular polygon Convex set Mathematics::Metric Geometry Convex combination Dual polyhedron Computer Science::Computational Geometry Dual polygon Condensed Matter Physics
Zdroj:	Philosophical Magazine Letters. 84:27-31
ISSN:	1362-3036 0950-0839
DOI:	10.1080/09500830310001621632
Popis:	We consider convex polyhedra which may be symmetrically inscribed in a sphere (‘T-polyhedra’). Incorporating elements of group theory, one of Courant's theorems and Weyl's expansion for the density of states, it is argued that a T-polyhedron quantum billiard and its dual of equal volume have equal emission frequencies. Application is made to the infinite set of convex ‘equilateral zonohedra’ quantum billiards. A thin-film resonant absorption experiment is proposed to verify these findings. It is found that, for dual convex regular polygons in , wave functions of the dual polygon in the related billiard problem maintain their functional form and, for duals of larger area, eigenvalues are lowered by a common scale factor.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::656de82c8d136c6eed9402d5751c68e2 https://doi.org/10.1080/09500830310001621632 Zobrazit plný text záznamu