Abstract
We describe scattering formalism to evaluate the Casimir energy of two gratings separated by a vacuum slit and the Casimir energy of two Chern- Simons layers in vacuum.
Highlights
The Casimir effect is a quantum fluctuation effect in the presence of boundaries [1] - [7]
In [8, 9] it was shown that the Casimir force of two flat Chern-Simons layers in vacuum can be both attractive and repulsive depending on values of constants in Chern-Simons actions
Repulsive Casimir forces appear in interaction of two Chern-Simons layers due to mixing of TE and TM modes during diffraction process
Summary
The Casimir effect is a quantum fluctuation effect in the presence of boundaries [1] - [7]. Systems with Chern-Simons terms on their surfaces have unique properties since a stable minimum of the Casimir energy naturally arises at nanoscales [12]; this feature should allow an effective experimental study of interactions beyond electromagnetism via the Casimir force measurements in future. The theory of two gratings with 1d spatial periodicity was developed in papers [13, 14], the Casimir free energy was expressed in terms of Rayleigh coefficients [15]. The approaches to evaluate the Casimir energy of gratings and ChernSimons layers are similar from the mathematical point of view. This similarity may be essential for better understanding of repulsive and attractive forces in the Casimir effect.
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