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arXiv · 1709.06284

Casimir energy of Sierpinski triangles

K. V. Shajesh·Prachi Parashar·Inés Cavero-Peláez·Jerzy Kocik·Iver Brevik
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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.

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K. V. Shajesh, Prachi Parashar, Inés Cavero-Peláez, Jerzy Kocik, Iver Brevik. 2017-09-19. Casimir energy of Sierpinski triangles. https://doi.org/10.1103/physrevd.96.105010

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