Casimir energy for $N$ constant conductivity $\delta$-plates with a neural network perception

TL;DR

This paper investigates the Casimir energy for multiple delta-function plates with constant conductivity, including graphene-like materials, using multiple scattering theory and neural networks to analyze many-body interactions and repulsive forces.

Contribution

It introduces a novel approach combining multiple scattering analysis with neural networks to study complex Casimir interactions involving many plates and different boundary conditions.

Findings

Neural networks can distinguish repulsive and attractive Casimir forces.

The multiple scattering parameter simplifies in the ideal boundary limit.

Boyer repulsion occurs between magnetic conductors and delta plates.

Abstract

The Casimir energy for $N$ $\delta$-function plates depends on the multiple scattering parameter $\Delta$. This $N$-body interaction was distributed into interactions with nearest neighbour scattering and next-to-nearest neighbour scattering based on partitions of $N-1$ 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 $\delta$ plates, which results in Boyer repulsion. In the asymptotic limit for ideal boundary conditions, the results become simple where the multiple scattering parameter $\Delta$ 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.