  Quantum-statistical effects occur during the propagation of electromagnetic
(EM) waves inside the dielectric media or metamaterials, which include a large
class of nanophotonic and plasmonic waveguides with dissipation and noise.
Exploiting the formal analogy between the Schrodinger equation and the Maxwell
equations for dielectric linear media, we rigorously derive the effective
Hamiltonian operator which describes such propagation. This operator turns out
to be essentially non-Hermitian in general, and pseudo-Hermitian in some
special cases. Using the density operator approach for general non-Hermitian
Hamiltonians, we derive a master equation that describes the statistical
ensembles of EM wave modes. The method also describes the quantum dissipative
and decoherence processes which happen during the wave's propagation, and,
among other things, it reveals the conditions that are necessary to control the
energy and information loss inside the above-mentioned materials.
