Can one count the shape of a drum?

Gnutzmann, Sven, Karageorge, Panos D. and Smilansky, Uzy 2006. Can one count the shape of a drum? Physical Review Letters 97 (9) , 090201. 10.1103/PhysRevLett.97.090201

Preview

PDF Download (206kB) | Preview

Abstract

Sequences of nodal counts store information on the geometry (metric) of the domain where the wave equation is considered. To demonstrate this statement, we consider the eigenfunctions of the Laplace-Beltrami operator on surfaces of revolution. Arranging the wave functions by increasing values of the eigenvalues, and counting the number of their nodal domains, we obtain the nodal sequence whose properties we study. This sequence is expressed as a trace formula, which consists of a smooth (Weyl-like) part which depends on global geometrical parameters, and a fluctuating part, which involves the classical periodic orbits on the torus and their actions (lengths). The geometrical content of the nodal sequence is thus explicitly revealed.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Mathematics
Additional Information:	4 pages.
Publisher:	American Physical Society
ISSN:	0031-9007
Last Modified:	15 May 2023 07:47
URI:	https://orca.cardiff.ac.uk/id/eprint/1798

Citation Data

Cited 24 times in Scopus. View in Scopus. Powered By Scopus® Data

Actions (repository staff only)

Edit Item