Stationary Two-State System in Optics using Layered Materials

When electrodynamics is quantized in a situation where the electrons exist only at a flat surface such as graphene, one of the Maxwell equations appears as a local part of the Hamiltonian. As a consequence of gauge invariance, any physical state has to be a zero-energy state of the local Hamiltonian. We construct two stationary quantum states; one reproduces scattering and absorption of light, which is familiar in classical optics and the other is more fundamentally related to photon creation. These two states are inseparable by the Hamiltonian and forming a two-state system, but there is a special number of surfaces for which two states are decoupled. The number is $2/\pi \alpha$ where $\pi \alpha$ is the absorption probability of single surface.Comment: 4 pages, 1 figur