Casimir energy of Sierpinski triangles
High Energy Physics - Theory
2017-12-01 v2
Abstract
Using scaling arguments and the property of self-similarity we derive the Casimir energies of Sierpinski triangles and Sierpinski rectangles. The Hausdorff-Besicovitch dimension (fractal dimension) of the Casimir energy is introduced and the Berry-Weyl conjecture is discussed for these geometries. We propose that for a class of fractals, comprising of compartmentalized cavities, it is possible to establish a finite value to the Casimir energy even while the Casimir energy of the individual cavities consists of divergent terms.
Cite
@article{arxiv.1709.06284,
title = {Casimir energy of Sierpinski triangles},
author = {K. V. Shajesh and Prachi Parashar and Inés Cavero-Peláez and Jerzy Kocik and Iver Brevik},
journal= {arXiv preprint arXiv:1709.06284},
year = {2017}
}
Comments
7 pages, 5 figures, minor typos corrected