Anomalous Casimir effect in axion electrodynamics

Understand

We study the Casimir effect in axion electrodynamics.

• A finite $\theta$-term affects the energy dispersion relation of photon if $\theta$ is time and/or space dependent.
• We focus on a special case with linearly inhomogeneous $\theta$ along the $z$-axis.
• Then we demonstrate that the Casimir force between two parallel plates perpendicular to the $z$-axis can be either attractive or repulsive, dependent on the gradient of $\theta$.