https://doi.org/10.1140/epjp/s13360-025-06436-4
Regular Article
Casimir energy for N constant conductivity 
-plates with a neural network perception
Qdit Labs Pvt. Ltd., 560092, Bengaluru, India
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Received:
28
December
2024
Accepted:
13
May
2025
Published online:
5
June
2025
Abstract
The Casimir energy for N-function plates depends on the multiple scattering parameter 
. This N-body interaction was distributed into interactions with nearest neighbour scattering and next-to-nearest neighbour scattering based on partitions of 
and its permutations. Implementing this methodology, we investigate the Casimir interaction for multiple plates with constant conductivity relatable to Graphene. We also study the Casimir energy between a perfect magnetic conductor and multiple constant conductivity plates, which results in Boyer repulsion. In the asymptotic limit for ideal boundary conditions, the results become simple where the multiple scattering parameter consists only of the nearest neighbour scattering term. Further, we used neural networks to analyze the Casimir energy in the Boyer repulsion configurations to understand the influence of pairwise energies on the many-body energy. The neural network could distinguish the repulsive and attractive forces depending on the regions of varying conductivity.
The original online version of this article was revised: in the originally published version of this article, the equation in the label of Fig. 1 was not displayed completely and was partially cut off. This issue had been raised by the author during the proofreading stage; however, it was not correctly implemented in the final published version.
The figure label has now been updated to display the equation in full and correctly. The original article has been corrected.
The publisher apologizes for this error and for any inconvenience caused.
A correction to this article is available online at https://doi.org/10.1140/epjp/s13360-026-07366-5.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2025
modified publication 2026
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
