Mesoscopic circuits with charge discreteness: Quantum transmission lines

We propose a quantum Hamiltonian for a transmission line with charge discreteness. The periodic line is composed of an inductance and a capacitance per cell. In every cell the charge operator satisfies a nonlinear equation of motion because of the discreteness of the charge. In the basis of one energy per site, the spectrum can be calculated explicitly. The incorporation of electrical resistance in the line has been considered briefly.