Mesoscopic circuits with charge discreteness:quantum transmission lines

Abstract

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. We consider briefly the incorporation of electrical resistance in the line.Comment: 11 pages. 0 figures. Will be published in Phys.Rev.