Hopfield dielectric

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In quantum mechanics, the Hopfield dielectric is a model of dielectric consisting of quantum harmonic oscillators interacting with the modes of the quantum electromagnetic field. The collective interaction of the charge polarization modes with the vacuum excitations, photons leads to the perturbation of both the linear dispersion relation of photons and constant dispersion of charge waves by the avoided crossing between the two dispersion lines of polaritons.^[1] Similar to the acoustic and the optical phonons and far from the resonance one branch is photon-like while the other charge is wave-like. The model was developed by John Hopfield in 1958.^[1]

Mathematically the Hopfield dielectric for the one mode of excitation is equivalent to the Trojan wave packet in the harmonic approximation. The Hopfield model of the dielectric predicts the existence of eternal trapped frozen photons similar to the Hawking radiation inside the matter with the density proportional to the strength of the matter-field coupling.